Method and apparatus for determining parameters and conditions for line of sight mimo communication

ABSTRACT

A method and apparatus determine parameters and conditions for line of sight MIMO communication. Reference signals can be received at a receiving device from a transmitting device. A channel matrix can be measured based on the reference signals. At least two of a first line of sight channel parameter, a second line of sight channel parameter, and a third line of sight channel parameter can be extracted based on the channel matrix. The first line of sight channel parameter can be based on transmitting device antenna element spacing. The second line of sight channel parameter can be based on a product of the transmitting device antenna element spacing and a receiving device antenna element spacing. The third line of sight channel parameter can be based on the receiving device antenna element spacing. The at least two line of sight channel parameters can be transmitted to the transmitting device.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to an application entitled “Method andApparatus for Determining Parameters and Conditions for Line of SightMIMO Communication,” Motorola Mobility docket number MM02042 and anapplication entitled “Method and Apparatus for Determining Parametersand Conditions for Line of Sight MIMO Communication,” Motorola Mobilitydocket number MM02043, both filed on even date herewith and commonlyassigned to the assignee of the present application, which are herebyincorporated by reference.

BACKGROUND 1. Field

The present disclosure is directed to a method and apparatus fordetermining parameters and conditions for line of sight Multiple InputMultiple Output (MIMO) communication.

2. Introduction

Presently, wireless communication devices communicate with othercommunication devices using wireless signals. Some communications, suchas streaming video, video conferencing, webcams, streaming audio, largefile transfers, and other data intensive communications, require highdata rates that have been typically difficult to achieve using standardwireless communication technologies. Multiple Input Multiple Output(MIMO) devices provide high data rates without increasing power andbandwidth. These MIMO devices use multiple transmit and receive antennasto increase the capacity of a communication system and achieve high datarates. Unfortunately, MIMO devices do not know all of the necessaryparameters and conditions for proper performance in a line of sightenvironment.

Thus, there is a need for a method and apparatus for determiningparameters and conditions for line of sight MIMO communication.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to describe the manner in which advantages and features of thedisclosure can be obtained, a description of the disclosure is renderedby reference to specific embodiments thereof which are illustrated inthe appended drawings. These drawings depict only example embodiments ofthe disclosure and are not therefore to be considered to be limiting ofits scope. The drawings may have been simplified for clarity and are notnecessarily drawn to scale.

FIG. 1 is an example illustration of an antenna configuration at atransmitter and a receiver according to a possible embodiment;

FIG. 2 is an example graph showing the size of a uniform linear antennaarray with four elements;

FIG. 3 is an example graph showing the size of a uniform linear antennaarray with eight elements;

FIG. 4 is an example flowchart illustrating the operation of a deviceaccording to a possible embodiment;

FIG. 5 is an example flowchart illustrating the operation of a deviceaccording to a possible embodiment;

FIG. 6 is an example flowchart illustrating the operation of a deviceaccording to a possible embodiment;

FIG. 7 is an example flowchart illustrating the operation of a deviceaccording to a possible embodiment;

FIG. 8 is an example flowchart illustrating the operation of a deviceaccording to a possible embodiment; and

FIG. 9 is an example block diagram of an apparatus according to apossible embodiment.

DETAILED DESCRIPTION

Embodiments provide a method and apparatus for determining parametersand conditions for line of sight Multiple Input Multiple Output (MIMO)communication. According to a possible embodiment, reference signals canbe received at a receiving device from a transmitting device. A channelmatrix can be measured based on the reference signals. At least two of afirst line of sight channel parameter, a second line of sight channelparameter, and a third line of sight channel parameter can be extractedbased on the channel matrix. The first line of sight channel parametercan be based on transmitting device antenna element spacing. The secondline of sight channel parameter can be based on a product of thetransmitting device antenna element spacing and a receiving deviceantenna element spacing. The third line of sight channel parameter canbe based on the receiving device antenna element spacing. The at leasttwo line of sight channel parameters can be transmitted to thetransmitting device.

According to another possible embodiment, a transmitter can transmitreference symbols from a regularly spaced subset of a set oftransmitting device antenna elements of the transmitter with elementsspanning one or more spatial dimensions. The transmitter can signaltransmit antenna element spacings in each dimension that can be used bythe transmitter for data transmission.

According to another possible embodiment, reference signals can bereceived from a transmitting device. Element spacings for each spatialdimension of an array of antennas at the transmitting device can bereceived. A channel matrix can be measured based on the referencesignals. A line of sight channel parameter for each element spacing foreach spatial dimension of the array of antennas at the transmittingdevice can be extracted based on the channel matrix. A spacing forantennas in the array of antennas in each spatial dimension can beselected that optimizes a capacity of a communication link.

According to another possible embodiment, reference signals can bereceived. A channel matrix can be measured based on the referencesignals. A least-squared error estimate of the parameter representingphase angles of the measured channel matrix can be determined. Asum-squared error can be calculated based on the least-squared errorestimate. The sum-squared error based on the least-squared errorestimate can be compared to a threshold. The measured channel matrix canbe ascertained to be classified as a line of sight multiple inputmultiple output channel based on comparing the sum-squared error basedon the least-squared error estimate to the threshold.

According to another possible embodiment, an indication can be receivedthat indicates a channel matrix is classified as a rank one line ofsight channel. The rank can also be estimated from the least squaredestimate of the phase angles. An indication of a phase difference ofreference signals transmitted from two different transmitter antennas toa single receive antenna can be received.

FIG. 1 is an example illustration 100 of an antenna configuration at atransmitter 110 and a receiver 120 according to a possible embodiment.The transmitter 110 and the receiver 120 can be any devices that cantransmit and receive signals. For example, the transmitter 110 and/orthe receiver 120 can be a User Equipment (UE), a base station, anenhanced Node B (eNB), a wireless terminal, a portable wirelesscommunication device, a smartphone, a cellular telephone, a flip phone,a personal digital assistant, a device having a subscriber identitymodule, a personal computer, a selective call receiver, a tabletcomputer, a laptop computer, an access point, or any other device thatis capable of sending and receiving communication signals on a wirelessnetwork.

The transmitter 110 can be assumed to be at the origin of the coordinatesystem and the receiver 120 can be on the x-axis and parallel to they-axis. The separation between the transmitter 110 and the receiver 120,such as the link range, is R and the inter-element spacing is d. Forderivation of a column orthogonality condition for line of sight MIMO,let y=Hx+w where y is the received signal vector, H is the channelmatrix, h_(m,n) is the element in the m-th row and i-th column of thematrix H and denotes the complex gain of the path from the n-th transmitelement to the m-th receive element, x is the transmitted signal vector,and w is the white noise. In a purely Line of Sight (LOS) channel, thechannel h_(m,n) is given by

$h_{m,n} = {\frac{\lambda}{4\pi \; p_{m,n}}{\exp\left( {{- j}\frac{2\pi}{\lambda}p_{m,n}} \right)}}$

where p_(m,n) is given by

$\begin{matrix}{p_{m,n} = \sqrt{R^{2} + \left( {{nd}_{T} - {md}_{R}} \right)^{2}}} \\{= {R\sqrt{1 + \frac{\left( {{nd}_{T} - {md}_{R}} \right)^{2}}{R^{2}}}}} \\{\approx {R\left( {1 + \frac{\left( {{nd}_{T} - {md}_{R}} \right)^{2}}{2R^{2}}} \right)}} \\{= {R + \frac{\left( {{nd}_{T} - {md}_{R}} \right)^{2}}{2R}}}\end{matrix}$

where R is the link range, □− and □¬ denote the distance betweenneighboring receive antennas and transmit antennas, and λ is thewavelength.

With this distance approximation, we have that

$h_{m,n} = {\frac{\lambda}{4\pi \; p_{m,n}}{{\exp\left( {{- j}\frac{2\pi}{\lambda}\left( {R + \frac{\left( {{nd}_{T} - {md}_{R}} \right)^{2}}{2R}} \right)} \right)}.}}$

A sufficient condition to maximize the capacity of the channel H is forthe columns to be orthonormal, such as both orthogonal and normalized.Note that with this condition, no precoding is needed to achieve channelcapacity, since the set of channels from the transmit antennas to thereceive array are orthogonal. This sufficient condition may or may notbe a necessary condition for the channel matrix H to have both full rankand equal magnitude eigenvectors.

The conditions for the columns to be orthonormal can be determined bytaking the inner product of the k-th and l-th columns of H. This innerproduct can be expressed as

$\begin{matrix}{{\langle{h_{\cdot {,k}},h_{\cdot {,l}}}\rangle} = {\left( \frac{\lambda}{4\pi} \right)^{2}{\sum\limits_{m = 0}^{N - 1}\; {\left( \frac{1}{p_{m,k}p_{m,l}} \right){\exp \left( {{- j}\frac{2\pi}{\lambda}\left( {p_{m,k} - p_{m,l}} \right)} \right)}}}}} \\{= {\left( \frac{\lambda}{4\pi} \right)^{2}{\sum\limits_{m = 0}^{N - 1}\; {\left( \frac{1}{p_{m,k}p_{m,l}} \right)\exp}}}} \\{\left( {{- j}\frac{2\pi}{\lambda}\left( {\left( {R + \frac{\left( {{kd}_{T} - {md}_{R}} \right)^{2}}{2R}} \right) - \left( {R + \frac{\left( {{ld}_{T} - {md}_{R}} \right)^{2}}{2R}} \right)} \right)} \right)} \\{= {\left( \frac{\lambda}{4\pi} \right)^{2}{\sum\limits_{m = 0}^{N - 1}\frac{\begin{matrix}{\exp\left( {{- j}\frac{2\pi}{\lambda}\left( {\left( {R + \frac{\left( {{kd}_{T} - {md}_{R}} \right)^{2}}{2R}} \right) -} \right.} \right.} \\\left. \left. \left( {R + \frac{\left( {{ld}_{T} - {md}_{R}} \right)^{2}}{2R}} \right) \right) \right)\end{matrix}}{\left( {R + \frac{\left( {{kd}_{T} - {md}_{R}} \right)^{2}}{2R}} \right)\left( {R + \frac{\left( {{ld}_{T} - {md}_{R}} \right)^{2}}{2R}} \right)}}}} \\{= {\left( \frac{\lambda}{4\pi} \right)^{2}{\sum\limits_{m = 0}^{N - 1}\frac{\exp \left( {{- j}\frac{\pi}{\lambda \; R}\left( {\left( {{kd}_{T} - {md}_{R}} \right)^{2} - \left( {{ld}_{T} - {md}_{R}} \right)^{2}} \right)} \right)}{\begin{matrix}{R^{2} + {\frac{1}{2}\left( {\left( {{kd}_{T} - {md}_{R}} \right)^{2} + \left( {{ld}_{T} - {md}_{R}} \right)^{2}} \right)} +} \\{\frac{1}{4R^{2}}\left( {{kd}_{T} - {md}_{R}} \right)^{2}\left( {{ld}_{T} - {md}_{R}} \right)^{2}}\end{matrix}}}}}\end{matrix}$

With the approximation that

${R^{2} + {\frac{1}{2}\left( {\left( {{kd}_{T} - {md}_{R}} \right)^{2} + \left( {{ld}_{T} - {md}_{R}} \right)^{2}} \right)} + {\frac{1}{4R^{2}}\left( {{kd}_{T} - {md}_{R}} \right)^{2}\left( {{ld}_{T} - {md}_{R}} \right)^{2}}} \approx R^{2}$

we have

$\begin{matrix}{{\langle{h_{\cdot {,k}},h_{\cdot {,l}}}\rangle} \approx {\left( \frac{\lambda}{4\pi \; R} \right)^{2}{\sum\limits_{m = 0}^{N - 1}\; {\exp \left( {{- j}\frac{\pi}{\lambda \; R}\left( {\left( {{kd}_{T} - {md}_{R}} \right)^{2} - \left( {{ld}_{T} - {md}_{R}} \right)^{2}} \right)} \right)}}}} \\{= {\left( \frac{\lambda}{4\pi \; R} \right)^{2}{\sum\limits_{m = 0}^{N - 1}\; \exp}}} \\{\left( {{- j}\frac{\pi}{\lambda \; R}\left( {{k^{2}d_{T}^{2}} - {2{kmd}_{T}d_{R}} + {m^{2}d_{R}^{2}} - {l^{2}d_{T}^{2}} + {2{lmd}_{T}d_{R}} - {m^{2}d_{R}^{2}}} \right)} \right)} \\{= {\left( \frac{\lambda}{4\pi \; R} \right)^{2}{\exp \left( {{- j}\frac{\pi}{\lambda \; R}\left( {{k^{2}d_{T}^{2}} - {l^{2}d_{T}^{2}}} \right)} \right)}{\sum\limits_{m = 0}^{N - 1}\; {\exp \left( {{- j}\frac{2\pi \; {md}_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)}}}} \\{= {\left( \frac{\lambda}{4\pi \; R} \right)^{2}{\exp \left( {{- j}\frac{\pi}{\lambda \; R}\left( {{k^{2}d_{T}^{2}} - {l^{2}d_{T}^{2}}} \right)} \right)}\frac{1 - \; {\exp \left( {{- j}\frac{2\pi \; {Nd}_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)}}{1 - {\exp \left( {{- j}\frac{2\pi \; d_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)}}}} \\{= {\left( \frac{\lambda}{4\pi \; R} \right)^{2}{{\exp \left( {{- j}\frac{\pi}{\lambda \; R}\left( {{k^{2}d_{T}^{2}} - {l^{2}d_{T}^{2}}} \right)} \right)} \cdot}}} \\{\frac{\begin{matrix}{{\exp \left( {{- 1}\frac{\pi \; {Nd}_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)}\left( {{\exp \left( {j\frac{\pi \; {Nd}_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)} - \exp} \right.} \\\left. \left( {{- j}\frac{\pi \; {Nd}_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right) \right)\end{matrix}}{\begin{matrix}{{\exp \left( {{- j}\frac{\pi \; d_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)}\left( {{\exp \left( {j\frac{\pi \; d_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)} - \exp} \right.} \\\left. \left( {{- j}\frac{\pi \; d_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right) \right)\end{matrix}}} \\{= {\left( {\left( \frac{\lambda}{4\pi \; R} \right)^{2}{\exp \left( {{- j}\frac{\pi}{\lambda \; R}\left( {{k^{2}d_{T}^{2}} - {l^{2}d_{T}^{2}}} \right)} \right)}} \right)\exp}} \\{{\left( {{- j}\frac{{\pi \left( {N - 1} \right)}d_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right) \cdot \frac{\sin \left( {\frac{\pi \; {Nd}_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)}{\sin \left( {\frac{\pi \; d_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)}}}\end{matrix}$

where N is the number of elements, such as antennas, in a transmit arrayof elements. So finally, we have

${\langle{h_{\cdot {,k}},h_{\cdot {,l}}}\rangle} \approx {\left( {\left( \frac{\lambda}{4\pi \; R} \right)^{2}{\exp \left( {{- j}\frac{\pi}{\lambda \; R}\left( {{k^{2}d_{T}^{2}} - {l^{2}d_{T}^{2}}} \right)} \right)}} \right){{\exp \left( {{- j}\frac{{\pi \left( {N - 1} \right)}d_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)} \cdot \frac{\sin \left( {\frac{\pi \; {Nd}_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)}{\sin \left( {\frac{\pi \; d_{T}d_{R}}{\lambda \; R}\left( {l - k} \right)} \right)}}}$

It can be noted that the multiplicative phase terms do not affect theinner product when the orthogonality condition applies.

For l=k, we have

${\langle{h_{\cdot {,k}},h_{\cdot {,k}}}\rangle} \approx {\left( \frac{\lambda}{4\pi \; R} \right)^{2}{N.}}$

The condition for all columns of H to be orthonormal (within a scalefactor) is that

${d_{T}d_{R}} = {\frac{\lambda \; R}{N}.}$

FIG. 2 is an example graph 200 showing the size of a uniform linearantenna array with four elements needed for the columns of H to beorthonormal as a function the distance between the transmitter andreceiver in meters, the carrier frequency in GHz, and the number ofantenna elements in the array under the assumption that d_(T)=d_(R)according to a possible embodiment.

FIG. 3 is an example graph 300 showing the size of a uniform linearantenna array with eight elements needed for the columns of H to beorthonormal as a function the distance between the transmitter andreceiver in meters, the carrier frequency in GHz, and the number ofantenna elements in the array under the assumption that d_(T)=d_(R)according to a possible embodiment.

As a first observation, there is no fundamental limit on the number ofdegrees of freedom N that can be achieved other than that

$\frac{N^{2}d_{T}^{2}}{2R^{2}}{\operatorname{<<}1}\mspace{14mu} {and}\mspace{14mu} \frac{N^{2}d_{R}^{2}}{2R^{2}}{\operatorname{<<}1}$

As a second observation, d_(T) and d_(R) need not be equal. Inparticular, if area is more constrained at one end of the link, such asat a receiving device like a UE, than at a transmitting device, such asat an eNB, then smaller spacing can be used at the UE and larger spacingcan be used at the eNB. For example, if the spacing of the elements atthe eNB is doubled, the spacing of the elements at the UE can be halved.

As a third observation, when the columns of H are orthonormal, noprecoding is needed to achieve channel capacity, and the power allocatedto the symbol transmitted from each transmit antenna element should beequal assuming the noise at the receiver is independent and identicallydistributed (i.i.d.).

As a fourth observation, if

${d_{T}d_{R}} = \frac{k\; \lambda \; R}{N}$

for integer k, then columns of H will be orthogonal.

As a fifth observation, alternatively, if

${d_{T}d_{R}} = \frac{\lambda \; R}{kN}$

for integer k, then the columns of H that are k apart will beorthogonal. In this case, the rank of H is no less than └N/K┘.

For the structure of a channel matrix for LOS-MIMO, the signal y_(k)received at the k-th antenna is given by

$y_{k} = {{\sum\limits_{l = 0}^{N - 1}\; {h_{k,l}x_{l}}} \approx {\sum\limits_{l = 0}^{N - 1}\; {\frac{\lambda}{4{\pi \left( {R + \frac{\left( {{ld}_{T} - {kd}_{R}} \right)^{2}}{2R}} \right)}}{\exp \left( {{- j}\frac{2\pi}{\lambda}\left( {R + \frac{\left( {{ld}_{T} - {kd}_{R}} \right)^{2}}{2R}} \right)} \right)}{x_{l}.}}}}$

Using the previous approximation that

$R \approx {R + \frac{\left( {{ld}_{T} - {kd}_{R}} \right)^{2}}{2R}}$

we have

$\begin{matrix}{y_{k} \approx {\frac{\lambda}{4\; \pi \; R}{\sum\limits_{l = 0}^{N - 1}{{\exp \left( {{- j}\frac{2\; \pi}{\lambda}\left( {R + \frac{\left( {{ld}_{T} - {kd}_{R}} \right)^{2}}{2R}} \right)} \right)}x_{l}}}}} \\{= {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi}{\lambda}\left( {R + \frac{k^{2}d_{R}^{2}}{2R}} \right)} \right)}{\sum\limits_{l = 0}^{N - 1}{{\exp \left( {j\frac{2\; \pi \; {lkd}_{T}d_{R}}{\lambda \; R}} \right)}{\exp \left( {{- j}\frac{\pi \; l^{2}d_{T}^{2}}{\lambda \; R}} \right)}x_{l}}}}} \\{= {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi \; R}{\lambda}} \right)}{\exp \left( {{- j}\frac{\pi \; k^{2}d_{R}^{2}}{\lambda \; R}} \right)}{\sum\limits_{l = 0}^{N - 1}{{\exp \left( {j\frac{2\; \pi \; {lkd}_{T}d_{R}}{\lambda \; R}} \right)}x_{l}^{\prime}}}}}\end{matrix}$

where

$x_{l}^{\prime} = {{\exp \left( {{- j}\frac{\pi \; l^{2}d_{T}^{2}}{\lambda \; R}} \right)}x_{l}}$

If we define the diagonal matrix B(z) to have diagonal elements given by

B _(i,j)(z)=exp(−jπi ² z)

then we have

$x^{\prime} = {{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}{x.}}$

We further define the matrix F(z) such that

F _(i,j)(z)=exp(j2πijz)

for 0≤i,j≤N−1, and the diagonal matrix A(z) having diagonal elementsgiven by

A _(i,j)(z)=exp(−jπi ² z).

With this notation, the received vector y=[y₀ y₁ . . . y_(N−1)]^(T) canbe expressed as

$\begin{matrix}{y \approx {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi \; R}{\lambda}} \right)}{A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}{F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}x}} \\{= {Hx}}\end{matrix}$

where the channel matrix H is given by

$H = {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi \; R}{\lambda}} \right)}{A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}{F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}.}}$

It can be noted that in the event that

${d_{T}d_{R}} = \frac{\lambda \; R}{N}$

the matrix

$F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)$

becomes the Inverse Discrete Fourier Transform (IDFT) matrix of lengthN. In this case, the channel is essentially performing the Inverse FastFourier Transform (IFFT) of the transmitted data, though the input andoutput of the IDFT are multiplied by diagonal matrices with unitmagnitude elements.

It can be shown that the singular values of H are equal to the singularvalues of

$F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)$

so that the singular values are completely determined by the value ofd_(T)d_(R)/λR and do not depend on the values of d_(T)/√{square rootover (λR)} and d_(R)/√{square root over (λR)} separately. The matricesA(d_(R) ²/λR) and B(d_(T) ²/λR) affect the left and right singularvectors of H, respectively, but do not affect the singular values.

The fundamental reason that LOS-MIMO works is that with the correctrange and frequency dependent antenna spacing, the signal from eachelement of the transmit array is seen to arrive from a differentdirection at the receive array. As a result, the phase progressionacross the receive array is different for each element of the transmitarray. With optimal spacing, this results in the received signal beingthe IDFT of the transmitted signal. Conversely, in the extreme farfield, each element of the transmit array is seen to arrive from thesame direction, and the phase progression across the receive array isthe same for each transmit element.

As a first observation, since

$y \approx {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi \; R}{\lambda}} \right)}{A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}{F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}x}$

it follows that the demodulated signal is given by

$x \approx {\frac{4\; \pi \; R}{\lambda}{\exp \left( {j\frac{2\; \pi \; R}{\lambda}} \right)}{B^{- 1}\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}{F^{- 1}\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{A^{- 1}\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}y}$

where A⁻¹ and B⁻¹ are diagonal matrices with unit magnitude elements andF⁻¹ is the DFT matrix when d_(T)d_(R)/λR=(1/N).

As a second observation, it can be observed that within a complex scalefactor, the matrix H is completely determined by three parameters

$\frac{d_{T}d_{R}}{\lambda \; R},\frac{d_{T}^{2}}{\lambda \; R},{{and}\mspace{14mu} {\frac{d_{R}^{2}}{\lambda \; R}.}}$

While the transmitter and receiver may know the spacing of theirelements, in the general case in which the linear arrays at thetransmitter and the receiver are not exactly aligned, it is not thedistance between elements that matters, but a projection of thisdistance that depends on the relative orientation of the linear arraysat the transmitter and the receiver. Furthermore, the transmitter andreceiver will not in general know the range R.

As a third observation, if U and V denote the left and right singularvectors of F, respectively, then the left and right singular vectors ofthe product

${A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}{F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}$

are given by the columns of Ũ and {tilde over (V)}, where

${\overset{\sim}{U} = {{A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}\mspace{11mu} U}},{{{and}\mspace{14mu} \overset{\sim}{V}} = {{B\left( \frac{- d_{T}^{2}}{\lambda \; R} \right)}\; {V.}}}$

It should be noted that the columns of {tilde over (V)} are the optimalset of precoders to use on the forward link, and the columns of Ũ arethe optimal set of precoders to use for the reverse link. Thus, it issufficient for the transmitter to be able to compute the Singular ValueDecomposition (SVD) of matrices of the form F(d_(T)d_(R)/λR), where thismatrix is an IFFT matrix if d_(T)d_(R)/λR=(1/N), and is otherwise aVandermonde matrix. In general, the transmitter only needs to know howto perform the SVD of a Vandermonde matrix.

As a fourth observation, the optimal precoders and power allocation forthe forward link only depend on knowledge of the parameters

$\frac{d_{T}d_{R}}{\lambda \; R}\mspace{14mu} {and}\mspace{14mu} \frac{d_{T}^{2}}{\lambda \; R}$

while the optimal precoders and power allocation for the reverse linkdepend on knowledge of the parameters

$\frac{d_{T}d_{R}}{\lambda \; R}\mspace{14mu} {and}\mspace{14mu} {\frac{d_{R}^{2}}{\lambda \; R}.}$

Again, while the transmitter may know the spacing of the elements d_(T)and the wavelength λ, the transmitter may not know the range, andfurthermore may not know the needed projection of this distance thatdepends on the relative orientation of the linear arrays at thetransmitter and the receiver.

There are multiple reasons it can be useful to be able to solve for theparameters of the LOS-MIMO channel. One reason it can be useful to beable to solve for these parameters is that when the singular values ofthe LOS-MIMO channel are equal, capacity can be achieved with anyorthogonal set of precoders. However, when the singular values are notequal, the optimal precoders and power allocation can depend on theparameters identified above. In general, the channel will rarely havethe normalized element spacing (normalized by the product of thewavelength and the range) needed for equal singular values, and so itcan be useful to solve for the parameters

$\frac{d_{T}d_{R}}{\lambda \; R},\frac{d_{T}^{2}}{\lambda \; R},{{and}\mspace{14mu} \frac{d_{R}^{2}}{\lambda \; R}}$

from the measured channel matrix in order to identify the optimal set ofprecoders, the rank that should be used, and the power allocation. Itcan be noted that even if the receiver knows the inter-element spacingof both the transmitter and the receiver, it will not in general knowthe range R. Also, even if the inter-element spacing and the range isknown, the projection of these distances onto the plane perpendicular tothe line between the transmitter and receiver may not be known, andfurthermore, the alignment of the projections of the linear array ontothis plane may also not be known. Therefore, it is unlikely that theparameters will be known at the transmitter and receiver, and as aresult, it can be useful for the parameters to be extracted from channelmeasurements.

Another reason it can be useful to be able to solve for the parametersof the LOS-MIMO channel is that even if the channel is LOS, in the casethat

$R\operatorname{>>}\frac{{Nd}_{T}d_{R}}{\lambda}$

the rank of the channel matrix will be approximately one, and LOS-MIMOwill not be possible. Thus it can be useful to determine when theLOS-MIMO condition exists.

Another reason it can be useful to be able to solve for the parametersof the LOS-MIMO channel is that for a Frequency Division Duplex (FDD)system, reciprocity may not be assumed due to the frequency differencebetween the forward and reverse links. However, for the MIMO LOScondition, the receiver can signal back to the transmitter that the LOScondition exists along with the parameters

$\frac{d_{T}d_{R}}{\lambda \; R},\frac{d_{T}^{2}}{\lambda \; R},{{and}\mspace{14mu} {\frac{d_{R}^{2}}{\lambda \; R}.}}$

Alternatively, if the LOS-MIMO condition exists on the received link, itcan be assumed to exist on the transmit link. Furthermore, theparameters for the transmit link can be calculated by correcting for thefrequency difference.

Another reason it can be useful to be able to solve for the parametersof the LOS-MIMO channel is that for a FDD system, the channel can becharacterized as (i) far-field LOS, (ii) LOS-MIMO, or (iii) fading(neither far-field LOS nor LOS-MIMO). Very little channel feedback isneeded for cases (i) and (ii). The optimal precoders for far-field LOSare already contained in the 3GPP standard (or nearly so). For theLOS-MIMO channel, the precoders can be determined by the values of theparameters

$\frac{d_{T}d_{R}}{\lambda \; R},\frac{d_{T}^{2}}{\lambda \; R},{{and}\mspace{14mu} {\frac{d_{R}^{2}}{\lambda \; R}.}}$

Note that it would not be necessary to signal the channel matrix or theeigenvectors of the channel matrix to the transmitter. Instead, it mayonly be necessary to signal the above parameters from the receiver tothe transmitter. Furthermore, the receiver can be able to determine theprecoders used by the transmitter from the parameter values that itsignaled to the transmitter. These values could be quantized in someagreed way. The receiver can signal, to the transmitter several bits toindicate that the channel is LOS-MIMO and quantized values of theparameters

$\frac{d_{T}d_{R}}{\lambda \; R},\frac{d_{T}^{2}}{\lambda \; R},{{and}\mspace{14mu} {\frac{d_{R}^{2}}{\lambda \; R}.}}$

It may only be necessary to signal two of the three parameters, as thethird parameter can be determined from the two other parameters usingthe relation

$\frac{d_{T}d_{R}}{\lambda \; R} = {\sqrt{\frac{d_{T}^{2}}{\lambda \; R}\frac{d_{R}^{2}}{\lambda \; R}}.}$

For a minimum least-squared error estimate of the LOS ChannelParameters, as noted above, for the LOS-MIMO channel the channel matrixis given by

$H = {\frac{\lambda}{4\pi \; R}{\exp\left( {{- j}\; \frac{2\pi \; R}{\lambda}} \right)}{A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}{F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}.}}$

Let the K×L matrix H denote the channel measured using referencesymbols, which is given by

Ĥ=H+N

and N is a K×L matrix of i.i.d. complex Gaussian random variables ofvariance σ². Let the K×L matrix ∠Ĥ denote phases of the elements of Ĥmeasured in radians. Let the (K−1)×L matrix Δ_(R)(∠Ĥ) denote the matrixwith k-th row equal to the result of subtracting the k-th row of ∠Ĥ fromthe k+1-th row of ∠Ĥ. The matrix Δ_(R)(∠Ĥ) can also be computed bydividing the k+1-th row of Ĥ by the k-th row of Ĥ and taking the phaseof each element of the resulting (K−1)×L matrix. The matrix Δ_(R)(∠Ĥ) isgiven by

${\Delta_{R}\left( {\angle \; \hat{H}} \right)} = {{{- \pi} \cdot \begin{bmatrix}\frac{d_{R}^{2}}{\lambda \; R} & {\frac{d_{R}^{2}}{\lambda \; R} - {2\frac{d_{T}d_{R}}{\lambda \; R}}} & \ldots & {\frac{d_{R}^{2}}{\lambda \; R} - {2\left( {L - 1} \right)\frac{d_{T}d_{R}}{\lambda \; R}}} \\{3\frac{d_{R}^{2}}{\lambda \; R}} & {{3\frac{d_{R}^{2}}{\lambda \; R}} - {2\frac{d_{T}d_{R}}{\lambda \; R}}} & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots \\{\left( {{2K} - 1} \right)\frac{d_{R}^{2}}{\lambda \; R}} & \ldots & \ldots & {{\left( {{2K} - 1} \right)\frac{d_{R}^{2}}{\lambda \; R}} - {2\left( {L - 1} \right)\frac{d_{T}d_{R}}{\lambda \; R}}}\end{bmatrix}} + N_{R}}$

where the K−1×L matrix N_(R) denotes the noise in the calculation of thephase differences between rows.

Let Δ_(R) ^(S)(∠Ĥ) denote the stacked columns of Δ_(R)(∠Ĥ), and letN_(R) ^(S) denote the stacked columns of N_(∠). We then have that

${\Delta_{R}^{S}\left( {\angle \; \hat{H}} \right)} = {{{- {{\pi \begin{bmatrix}1 & 0 \\3 & 0 \\\vdots & \vdots \\{{2K} - 1} & 0 \\1 & {- 2} \\3 & {- 2} \\\vdots & \vdots \\{{2K} - 1} & {- 2} \\\vdots & \vdots \\\vdots & \vdots \\\vdots & \vdots \\\vdots & \vdots \\1 & {{- 2}\left( {L - 1} \right)} \\3 & {{- 2}\left( {L - 1} \right)} \\\vdots & {{- 2}\left( {L - 1} \right)} \\{{2K} - 1} & {{- 2}\left( {L - 1} \right)}\end{bmatrix}}\begin{bmatrix}\frac{d_{R}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}}} + N_{R}^{S}} = {{W_{R}\begin{bmatrix}\frac{d_{R}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}} + N_{R}^{S}}}$

where the (K−1)L×2 matrix W_(R) is implicitly defined from the aboveequation.

This system of equation is highly over-determined since we have (K−1)Lequations with only two unknowns. With the formulation, theleast-squared error estimate of the parameters

$\frac{d_{T}d_{R}}{\lambda \; R}\mspace{14mu} {and}\mspace{14mu} \frac{d_{R}^{2}}{\lambda \; R}$

is given by

$\begin{bmatrix}\frac{d_{R}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}_{LSE} = {\left( {W_{R}^{H}W_{R}} \right)^{- 1}W_{R}^{H}{{\Delta_{R}^{S}\left( {\angle \; \hat{H}} \right)}.}}$

The sum Mean-Squared Error (MSE) of the least-squares estimate is givenby

${{MSE}\left( \begin{bmatrix}\frac{d_{R}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}_{LSE} \right)} = {{E\left\lbrack {\left( N_{R}^{S} \right)^{H}W_{R}^{H}W_{R}N_{R}^{S}} \right\rbrack}.}$

Evaluation of the sum mean-squared error can depend on knowledge of thejoint statistics of the noise vector N_(R) ^(S) which may be difficultto estimate. Alternatively, the Sum-Squared Error (SSE) of theleast-squared error estimate can be directly computed as

${{SSE}\left( \begin{bmatrix}\frac{d_{R}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}_{LSE} \right)} = {\left( {\Delta_{R}^{S}\left( {\angle \; \hat{H}} \right)} \right)^{H}\left( {I_{{({K - 1})}L} - {{W_{R}\left( {W_{R}^{H}W_{R}} \right)}^{- 1}W_{R}^{H}}} \right){\Delta_{R}^{S}\left( {\angle \; \hat{H}} \right)}}$

where I_((K−1)L) denotes a square identity matrix of dimension (K−1)L.It should be noted that since the matrix W_(R) does not depend on themeasured channel, the matrix W_(R)(W_(R) ^(H)W_(R))⁻¹W_(R) ^(H) can bepre-computed. The computed sum-squared error can be compared to athreshold to determine whether or not the measured channel Ĥ can beproperly classified as an LOS-MIMO channel.

The procedure for jointly estimating the parameters

$\frac{d_{T}d_{R}}{\lambda \; R}\mspace{14mu} {and}\mspace{14mu} \frac{d_{T}^{2}}{\lambda \; R}$

is very similar to the method above for jointly estimating

$\frac{d_{T}d_{R}}{\lambda \; R}\mspace{14mu} {and}\mspace{14mu} {\frac{d_{R}^{2}}{\lambda \; R}.}$

To begin, let the matrix K×(L−1) matrix Δ_(C)(∠Ĥ) denote the matrix withk-th row equal to the result of subtracting the l-th column of ∠Ĥ fromthe l+1-th column of ∠Ĥ. The matrix Δ_(C)(∠Ĥ) can also be computed bydividing the l+1-th column of Ĥ by the l-th column of Ĥ and taking thephase of each element of the resulting K×(L−1) matrix. The matrixΔ_(C)(∠Ĥ) is given by

${\Delta_{C}\left( {\angle \hat{H}} \right)} = {{- {\pi \begin{bmatrix}{\frac{d_{T}^{2}}{\lambda \; R} - {2\frac{d_{T}d_{R}}{\lambda \; R}}} & {{3\frac{d_{T}^{2}}{\lambda \; R}} - {2\frac{d_{T}d_{R}}{\lambda \; R}}} & \ldots & {{\left( {{2L} - 1} \right)\frac{d_{T}^{2}}{\lambda \; R}} - {2\frac{d_{T}d_{R}}{\lambda \; R}}} \\{\frac{d_{T}^{2}}{\lambda \; R} - {4\frac{d_{T}d_{R}}{\lambda \; R}}} & {{3\frac{d_{T}^{2}}{\lambda \; R}} - {4\frac{d_{T}d_{R}}{\lambda \; R}}} & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots \\{\frac{d_{T}^{2}}{\lambda \; R} - {2K\frac{d_{T}d_{R}}{\lambda \; R}}} & \ldots & \ldots & {{\left( {{2L} - 1} \right)\frac{d_{T}^{2}}{\lambda \; R}} - {2K\frac{d_{T}d_{R}}{\lambda \; R}}}\end{bmatrix}}} + N_{C}}$

where the K−1×L matrix N_(C) denotes the noise in the calculation of thephase differences between columns.

Let Δ_(C) ^(S)(∠Ĥ) denote the stacked columns of Δ_(C)(∠Ĥ), and letN_(C) ^(S) denote the stacked columns of N_(C). We then have that

${\Delta_{C}^{S}\left( {\angle \hat{H}} \right)} = {{{- {{\pi \begin{bmatrix}1 & {- 2} \\1 & {- 4} \\\vdots & \vdots \\1 & {{- 2}K} \\3 & {- 2} \\3 & {- 4} \\\vdots & \vdots \\3 & {{- 2}K} \\\vdots & \vdots \\\vdots & \vdots \\\vdots & \vdots \\\vdots & \vdots \\{{2L} - 1} & {- 2} \\{{2L} - 1} & {- 4} \\\vdots & \vdots \\{{2L} - 1} & {{- 2}K}\end{bmatrix}}\begin{bmatrix}\frac{d_{T}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}}} + N_{C}^{S}} = {{W_{C}\begin{bmatrix}\frac{d_{T}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}} + N_{C}^{S}}}$

where the K(L−1)×2 matrix W_(C) is implicitly defined from the aboveequation. Following the analysis above, the least-squared error estimateof the parameters

$\frac{d_{T}d_{R}}{\lambda \; R}\mspace{14mu} {and}\mspace{14mu} \frac{d_{T}^{2}}{\lambda \; R}$

is given by

$\begin{bmatrix}\frac{d_{T}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}_{LSE} = {\left( {W_{C}^{H}W_{C}} \right)^{- 1}W_{C}^{H}\; {\Delta_{C}^{S}\left( {\angle \hat{H}} \right)}}$

The sum mean-squared error (MSE) of the least-squares estimate is givenby

${{MSE}\left( \begin{bmatrix}\frac{d_{T}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}_{LSE} \right)} = {{E\left\lbrack {\left( N_{C}^{S} \right)^{H}W_{C}^{H}W_{C}N_{C}^{S}} \right\rbrack}.}$

Evaluation of the sum mean-squared error can depend on knowledge of thejoint statistics of the noise vector N_(C) ^(S) which may be difficultto estimate. Alternatively, the SSE of the least-squared error estimatecan be directly computed as

${{SSE}\left( \begin{bmatrix}\frac{d_{T}^{2}}{\lambda \; R} \\\frac{d_{T}d_{R}}{\lambda \; R}\end{bmatrix}_{LSE} \right)} = {\left( {\Delta_{C}^{S}\left( {\angle \hat{H}} \right)} \right)^{H}\left( {I_{{({L - 1})}K} - {{W_{C}\left( {W_{C}^{H}W_{C}} \right)}^{- 1}W_{C}^{H}}} \right){\Delta_{C}^{S}\left( {\angle \hat{H}} \right)}}$

where I_((K−1)L) denotes a square identity matrix of dimension (L−1)K.It should be noted that since the matrix W_(C) does not depend on themeasured channel, the matrix W_(C)(W_(C) ^(H)W_(C))⁻¹W_(C) ^(H) can bepre-computed. The computed sum-squared error can be compared to athreshold to determine whether or not the measured channel Ĥ can beproperly classified as an LOS-MIMO channel.

It should be noted that with the two estimators, we now have twoestimates for the parameter

$\frac{d_{T}d_{R}}{\lambda \; R}.$

Several possibilities exist for choosing the best estimate of thisparameter, and these include at least averaging the two estimates andchoosing the estimate for which the least-squares error is smaller.

It may also be beneficial to iterate between the two estimators and usethe first estimate for this parameter from the first estimator as ininput to the second estimator, where the second estimator is modified tocompute the least-squares estimate of the second parameter givenknowledge of the first parameter.

According to a possible embodiment, for a Time Division Duplex (TDD)system, channel reciprocity should apply, so the forward channel can belearned from reference symbols sent on the reverse channel In this casethere is no need for the transmitter to explicitly extract theparameters

$\frac{d_{T}d_{R}}{\lambda \; R}\mspace{14mu} {and}\mspace{14mu} \frac{d_{T}^{2}}{\lambda \; R}$

since it can measure H^(T) from the reverse link reference symbols, andsubsequently compute the right singular vectors of H. For an FDD system,if the wavelength of the forward link is λ₁, and the wavelength of thereverse link is λ₂, then the transmitter measures H^(T)(λ₂) on thereverse link and can compute H(λ₁).

In the absence of noise, the parameters

$\frac{d_{T}d_{R}}{\lambda_{2}R},\frac{d_{T}^{2}}{\lambda_{2}R},{{and}\mspace{14mu} \frac{d_{R}^{2}}{\lambda_{2}R}}$

can be determined exactly from H^(T)(λ₂). With additive noise, aleast-squares and/or iterative formulation can be used to solve forthese parameters. From these parameters, the H(λ₁) parameters can becomputed as

$\frac{d_{T}d_{R}}{\lambda_{1}R} = {\left( \frac{\lambda_{2}}{\lambda_{1}} \right)\left( \frac{d_{T}d_{R}}{\lambda_{2}R} \right)}$$\frac{d_{T}^{2}}{\lambda_{1}R} = {\left( \frac{\lambda_{2}}{\lambda_{1}} \right)\left( \frac{d_{T}^{2}}{\lambda_{2}R} \right)}$$\frac{d_{R}^{2}}{\lambda_{2}R} = {\left( \frac{\lambda_{2}}{\lambda_{1}} \right){\left( \frac{d_{R}^{2}}{\lambda_{2}R} \right).}}$

According to another possible related embodiment, in an FDD system, letthe receiver solve for

$\frac{d_{T}d_{R}}{\lambda_{1}R}\mspace{14mu} {and}\mspace{14mu} \frac{d_{T}^{2}}{\lambda_{1}R}$

from H(λ₁) measured using reference symbols and signal these tworeal-valued parameters back to the transmitter. This is all theinformation the transmitter needs in order to determine both thesingular values and the singular vectors used to optimize channelcapacity.

According to another possible related embodiment, the transmitter and/orreceiver can have some ability to control the element spacing. One suchexample can be the case of a linear array that can be rotated as awhole. An alternative example can be a case of a larger array for whichonly a subset of the elements are used.

The receiver can measure the forward channel H from reference symbolssent on the forward channel. From the measured H, the receiver can solvefor

$\frac{d_{T}d_{R}}{\lambda \; R}$

and this value can be signaled to the transmitter. Alternatively, thetransmitter can solve for

$\frac{d_{T}d_{R}}{\lambda \; R}$

using reference symbols transmitted on the reverse link.

The transmitter and/or receiver can then adjust the rotation of thearray to improve the spacing of the elements relative to the orientationof the transmitter and receiver. Alternatively, the transmitter and/orreceiver can change the subset of antenna elements (from a presumedlarger array) which are used to transmit and/or receive. If only one ofthe transmitter and/or receiver have the ability to change the effectiveinter-element spacing, then this can be done without collaborationbetween the devices. Alternatively, if both the transmitter and thereceiver have the capability to adjust the inter-element spacing, thenthe transmitter and the receiver can agree on how each will adjust itsspacing to optimize the parameter

$\frac{d_{T}d_{R}}{\lambda \; R}.$

According to another possible related embodiment, it may be that thesmall cell eNB or Access Point (AP) has K antennas while the UE has Lantennas, where K>L. The UE can then determine the subset of L eNB or APantennas which yields the best LOS capacity and signal this set back tothe eNB or AP.

According to another possible related embodiment, the eNB and the UE canhave some flexibility in the selection of the frequency over which theyoperate. The receiver can measure the channel H(λ₁) using referencessymbols. From this, the receiver can extract the parameter

$\frac{d_{T}d_{R}}{\lambda_{1}R}$

Given a set of additional allowed frequencies λ₂, λ₃, . . . , λ_(N), thereceiver can then evaluate the parameter over this set in the followingmanner

$\frac{d_{T}d_{R}}{\lambda_{k}R} = {\left( \frac{\lambda_{1}}{\lambda_{k}} \right)\frac{d_{T}d_{R}}{\lambda_{1}R}}$

and then can select the wavelength λ* from this set which yields thechannel H(λ*) with the largest capacity. The set of allowed frequenciescan be known by the receiver or can be signaled from the transmitter.Alternatively, the receiver can signal

$\frac{d_{T}d_{R}}{\lambda_{1}R}$

to the transmitter and let the transmitter perform the frequencyoptimization.

According to another possible related embodiment, the transmitter cantransmit reference symbols over a regularly spaced subset of itsantennas. The receiver can then measure

$\frac{d_{T}d_{R}}{\lambda \; R}$

from this regularly spaced subset. The transmitter can inform thereceiver of the additional transmit element spacings that can be used bythe transmitter, where this information can be signaled in the form ofratios to the spacing that was used for the references symbols. Forexample, the transmitter can signal that transmit element spacings equalto one-half and twice the spacing of that used for the reference symbolsare possible. The receiver can compute

$\frac{k_{i}d_{T}d_{R}}{\lambda \; R}$

for each allowed scaling of the spacing k_(i), and can signal thespacing that maximizes channel capacity back to the transmitter.Alternatively, the receiver can signal the measurement

$\frac{d_{T}d_{R}}{\lambda \; R}$

to the transmitter, and the transmitter can select the scaling k_(i) ofthe element spacing that maximizes channel capacity.

The parameters

$\frac{d_{T}d_{R}}{\lambda \; R},\frac{d_{T}^{2}}{\lambda \; R},{{and}\mspace{14mu} \frac{d_{R}^{2}}{\lambda \; R}}$

can be computed, for example, with the least-squared error method givenabove, as long as the receiver receives reference symbols from at leasttwo transmit antennas. The parameters are then known for the spacing ofthe elements that were used, and the parameters for any other allowedelement spacing at the transmitter or the receiver can be determinedfrom these measurements.

According to another possible related embodiment, in the case that thetransmitter has uniform linear arrays spanning multiple dimensions, thetransmitter can transmit reference symbols from a regularly spacedsubset of the elements in each dimension. The transmitter can alsoinform the receiver of the additional transmit element spacings that canbe used by the transmitter for each dimension, where this informationcan be signaled in the form of ratios to the spacing that was used forthe references symbols. The receiver can then measure

$\frac{d_{T}d_{R}}{\lambda \; R}$

for each dimension. The receiver then can compute this parameter foreach allowed element spacing for each dimension of the transmit arrayand can select the spacing for each dimension which optimizes thecapacity. Alternatively, receiver can measure

$\frac{d_{T}d_{R}}{\lambda \; R}$

from reference symbols transmitted from the regularly spaced subset ofthe elements in each dimension, and can signal these measurements backto the transmitter. The transmitter then can select the element spacingin each dimension that maximizes the link capacity.

According to another possible related embodiment, in the case ofCoOrdinated Multi-Point (COMP) transmission points or remoteradio-heads, the transmission points can be selected for which theparameter

$\frac{d_{T}d_{R}}{\lambda \; R}$

is most nearly equal to 1/N or an integer multiple of 1/N, or moregenerally, for which the resulting LOS channel capacity is maximized.For this case d_(T) is the distance between transmission points,possibly projected onto a line orthogonal to a line between the midpointof the transmission points and the receiver.

According to another possible related embodiment, in the case that

$\frac{d_{T}d_{R}}{\lambda \; R} = \frac{1}{N}$

channel H has full rank and the singular values are all equal. In thiscase full rank transmission can be used. Furthermore, there is norestriction on the precoders, as any orthonormal set of precoders canachieve capacity. In this case, it is possible to enable a simplifiedreceiver by inverting the channel and taking the DFT of the data priorto transmission. The output of the DFT can have the same average poweras its input, but the peak power can significantly greater. Conversely,the diagonal matrices have no impact on peak or average power as thediagonal elements all have unit magnitude.

If the input to the channel is the transform x′ of x defined as

${x^{\prime} = {{B^{- 1}\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}{F^{- 1}\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{A^{- 1}\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}x}},$

then the output of the channel is given by

$\begin{matrix}{y = {\frac{\lambda}{4\pi \; R}{\exp\left( {{- j}\; \frac{2\pi \; R}{\lambda}} \right)}{A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}{F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}x^{\prime}}} \\{= {\frac{\lambda}{4\pi \; R}{\exp\left( {{- j}\; \frac{2\pi \; R}{\lambda}} \right)}{A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}{F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}{B^{- 1}\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}F^{- 1}}} \\{{\left( \frac{d_{T}d_{R}}{\lambda \; R} \right){A^{- 1}\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}x}} \\{{= {\frac{\lambda}{4\pi \; R}{\exp\left( {{- j}\; \frac{2\pi \; R}{\lambda}} \right)}x}},}\end{matrix}$

so that the output of the channel is equal to the data x multiplied by acomplex scalar.

According to another possible related embodiment, based on measurementsof the channel Ĥ using reference symbols, the channel can be classifiedas a channel type and channel parameters can be sent that correspond tothe channel type. For example, as mentioned above, the channel can beclassified as (i) rank one LOS, (ii) LOS-MIMO, or (iii) fading (neither(i) or (ii)).

If the receiver determines that the channel is rank one LOS, it cansignal rank one LOS to the transmitter. It can then measure the phasedifference of the reference symbols transmitted from two differentantennas when measured at a single receive antenna. With thisinformation, the transmitter can co-phase the signals from the twotransmit antennas to arrive in phase at the receiver. As noted above,only two reference symbols are required to determine the phasing for anynumber of transmit antennas so long the distance of each additionalantenna element from one of the antennas used to transmit the referencesymbols is known, though this distance can be normalized by the distancebetween the two antennas used to transmit the two reference symbols.

If the receiver determines the channel is LOS-MIMO, it can signal backLOS-MIMO to the transmitter along with the coefficients

$\frac{d_{T}d_{R}}{\lambda \; R}\mspace{14mu} {and}\mspace{14mu} \frac{d_{T}^{2}}{\lambda \; R}$

If the receive determines that the channel is neither rank one LOS norLOS-MIMO, the receiver can signal this back to the transmitter. Thereceiver can also signal back the channel measurements, and/or theprecoder and rank to use for transmission. For an extension of the abovecase to a planar array with N×N antennas with total of N² antennas perplanar array, using a Taylor series approximation as in the uniformlinear array case, we get

${H_{{{2{d\_ Nm}_{1}} + m_{2}},{{Nn}_{1} + n_{2}}} = {\frac{\lambda}{4\pi \; R}{\exp\left( {{- j}\frac{2\pi}{\lambda}\left( {R + \frac{\left( {{n_{1}d_{T}} - {m_{1}d_{R}}} \right)^{2}}{2R} + \frac{\left( {{n_{2}d_{T}} - {m_{2}d_{R}}} \right)^{2}}{2R}} \right)} \right)}}},$

where N is the number of antennas in each dimension, where (m₁, m₂) arethe co-ordinates of receiver array and (n₁, n₂) are the coordinates ofthe transmitter array. One restriction on this equation can be that thex and y axes of the first array are parallel with the x and y axes ofthe second array (note that with this restriction, the planes containingthe arrays are parallel).

It can be easily seen that if we discard the terms λ/4πR and exp(−j2πR/λ) since these terms are scalars and are the same for all theelements of the matrices then new matrix H_(2d) for the planar case isthe Kronecker product of matrices corresponding to uniform linear arraycase, i.e,

H_(2d)=H⊗H.

It can be noted that if Ĥ_(2d) is measurement of the N²×N² channel basedon reference symbols, then the N×N sub-matrix

$H_{{{2{d\_ Nm}_{1}} + m_{2}},{{Nm}_{1} + n_{2}}} = {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi}{\lambda}\left( {R + \frac{\left( {{n_{2}d_{T}} - {m_{2}d_{R}}} \right)^{2}}{2R}} \right)} \right)}}$

for n₁=m₁ is a measurement of Ĥ, for each value of m₁. Since there are Nsuch measurements, these measurements can be averaged to form animproved average {circumflex over (Ĥ)}. Similarly, the N×N sub-matrix

$H_{{{2{d\_ Nm}_{1}} + m_{2}},{{Nn}_{1} + n_{2}}} = {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi}{\lambda}\left( {R + \frac{\left( {{n_{2}d_{T}} - {m_{1}d_{R}}} \right)^{2}}{2R}} \right)} \right)}}$

for n₂=m₂ is also a measurement of Ĥ, for each value of m₂. Since thereare N such measurements, these measurements can be averaged to form animproved average {circumflex over (Ĥ)}. Furthermore, first and secondestimates can be averaged to form an improved estimate.

As indicated previously in the case of one-dimensional arrays, the threeparameters

$\frac{d_{T}d_{R}}{\lambda \; R},\frac{d_{T}^{2}}{\lambda \; R},{{and}\mspace{14mu} \frac{d_{R}^{2}}{\lambda \; R}}$

can be estimated from the measurements of {circumflex over (Ĥ)}.Finally, the full N²×N² channel H_(2d) can be completely specified fromany two of these three parameters, since any two parameters can be usedto generate the third parameter. Thus, it may be only necessary tosignal two parameters back to the transmitter to fully specify thechannel.

The singular values of H_(2d) are the all possible product pairs of thesingular values of H and the left singular vectors are obtained usingthe Kronecker product of the left singular vectors of H and the rightsingular vectors are obtained using the Kronecker product of rightsingular vectors of H. It can be thus seen that all the ideas relevantfor the uniform linear array can be easily extended to the planar array.Since the eigenvectors of a planar array are the Kronecker product ofthe eigenvectors of the linear array, one of the advantages of theplanar array is that we can perform a singular value decomposition overa much smaller matrix.

For the case

${\frac{d_{T}d_{R}}{\lambda \; R} = \frac{1}{N}},$

all the eigenvalues of H have unit magnitude and hence all theeigenvalues of H_(2d) are also of unit magnitude. The matrix H_(2d) hasN² unit magnitude eigenvalues while H has only N unit magnitudeeigenvalues.

Let us now compare the dimensions of a uniform linear array with aplanar array such that they have the same capacity (same number of unitmagnitude eigenvalues). The system is supposed to be designed as optimumfor a given distance R. Let L_(Tu) and L_(Ru) be the linear dimension ofthe Uniform Linear Array (ULA) transmitter and receiver, respectively,and L_(Tp)×L_(Tp), and L_(Rp)×L_(Rp) be the dimensions of the planararray transmitter and receiver, respectively. For equal capacity bothsystems should have equal number of antennas thus there are N² antennain the ULA. It can be shown using d_(Tu)=L_(Tu)/(N²−1) andd_(Tp)=L_(Tp)/(N−1) that:

${{L_{Tu}L_{Ru}} = {\frac{\left( {N + 1} \right)^{2}}{N}L_{T_{P}}L_{R_{P}}}},$

thus, the dimension of linear array should be sqrt(N) times the lineardimension of the planar array. The max distance from the center of theantenna array to the farthest antenna is sqrt(N/2) times more in alinear array than in a planar array. Hence, it is more likely for alinear array to not satisfy the constraints used for the distanceapproximations used to determine the phase of the different signal pathsto be correct

$\frac{N^{2}d_{T}^{2}}{2R^{2}}\mspace{11mu} {\operatorname{<<}1}\mspace{14mu} {and}\mspace{14mu} \frac{N^{2}d_{R}^{2}}{2R^{2}}\mspace{11mu} {\operatorname{<<}1}$

For a general orientation of linear arrays, the distance r_(m,n) betweenthe m-th element of the first array and the n-th element of the secondarray can be expressed as

$\begin{matrix}{r_{m,n} = \begin{bmatrix}{\left( {R + {{md}_{R}\sin \; \theta_{r}\cos \; \varphi_{r}} - {{nd}_{t}\sin \; \theta_{t}}} \right)^{2} + \left( {{md}_{R}\sin \; \theta_{r}\sin \; \varphi_{r}} \right)^{2} +} \\\left( {{{md}_{R}\cos \; \theta_{r}} - {{nd}_{t}\cos \; \theta_{t}}} \right)^{2}\end{bmatrix}^{1/2}} \\{= {R\;\begin{bmatrix}{\left( {1 + {R^{- 1}\left( {{{md}_{R}\sin \; \theta_{r}\cos \; \varphi_{r}} - {{nd}_{T}\sin \; \theta_{t}}} \right)}} \right)^{2} + {R^{- 2}\left( {{md}_{R}\sin \; \theta_{r}\sin \; \varphi_{r}} \right)}^{2}} \\{R^{- 2}\left( {{{md}_{R}\cos \; \theta_{r}} - {{nd}_{T}\cos \; \theta_{t}}} \right)}^{2}\end{bmatrix}}^{1/2}} \\{\approx {R\begin{bmatrix}{1 + {m^{2}d_{R}^{2}{R^{- 2}\left( {{\sin^{2}\theta_{r}\sin^{2}\varphi_{r}} + {\cos^{2}\theta_{r}}} \right)}} + {n^{2}d_{T}^{2}R^{- 2}\cos^{2}\theta_{t}} -} \\{{2\; {mnd}_{R}d_{T}R^{- 2}\cos \; \theta_{r}\cos \; \theta_{t}} + {2\; {md}_{R}R^{- 1}\sin \; \theta_{r}\cos \; \varphi_{r}} -} \\{2{nd}_{T}R^{- 1}\sin \; \theta_{t}}\end{bmatrix}}^{1/2}} \\{= {R\;\begin{bmatrix}{1 + {R^{- 2}\left( {{m^{2}{d_{R}^{2}\left( {{\sin^{2}\theta_{r}\sin^{2}\varphi_{r}} + {\cos^{2}\theta_{r}}} \right)}} + {n^{2}d_{T}^{2}\cos^{2}\theta_{t}}} \right)} -} \\{{2\; {mnd}_{R}d_{T}R^{- 2}\cos \; \theta_{r}\cos \; \theta_{t}} + {2{md}_{R}R^{- 1}\sin \; \theta_{r}\cos \; \varphi_{r}} - {2{nd}_{T}R^{- 1}\sin \; \theta_{t}}}\end{bmatrix}}^{1/2}} \\{= {R\begin{bmatrix}{1 + {R^{- 2}\left( {{m^{2}{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}} + {n^{2}d_{T}^{2}\cos^{2}\theta_{t}}} \right)} -} \\{{2{mnd}_{R}d_{T}R^{- 2}\cos \; \theta_{r}\cos \; \theta_{t}} + {2{md}_{R}R^{- 1}\sin \; \theta_{r}\cos \; \varphi_{r}} - {2{nd}_{T}R^{- 1}\sin \; \theta_{t}}}\end{bmatrix}}^{1/2}} \\{\approx {R + {\frac{1}{2R}m^{2}{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}} + {\frac{1}{2R}n^{2}d_{T}^{2}\cos^{2}\theta_{t}} -}} \\{{{\frac{1}{R}{mnd}_{R}d_{T}\cos \; \theta_{r}\cos \; \theta_{t}} + {{md}_{R}\sin \; \theta_{r}\cos \; \varphi_{r}} - {{nd}_{T}\sin \; \theta_{t}}}}\end{matrix}$

for appropriately defined angles θ_(t), θ_(r), and ϕ_(r).

In the special case that all of these angles are zero, the two lineararrays are parallel and are also perpendicular to the line connectingthe endpoints of the arrays, then we have that

$r_{m,n} \approx {R + {\frac{1}{2R}\left( {{m^{2}d_{R}^{2}} + {n^{2}d_{T}^{2}}} \right)} - {\frac{1}{R}\; {mnd}_{R}d_{T}}}$

and the channel matrix can be expressed as

$H = {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi \; R}{\lambda}} \right)}{A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}{F\left( \frac{d_{T}d_{R}}{\lambda \; R} \right)}{{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}.}}$

For example, the channel matrix can have the same form as above, A×F×B,where A and B can be diagonal matrices, and F can be an IDFT matrix thatis possibly oversampled. Also, only three parameters may be required andthe third parameter can be determined from any two of the threeparameters. Also, as above, the receiver can solve for the threeparameters from the measured channel matrix H.

For a slightly more general case, the two linear arrays lie in planesthat are perpendicular to the line connecting the endpoints of thearrays. In this case, the angles θ_(t) and ϕ_(r) have values θ_(t)=0ϕ_(r)=±π/2, and the distance between elements of the two arrays is givenby

$r_{m,n} \approx {R + {\frac{1}{2R}\left( {{m^{2}d_{R}^{2}} + {n^{2}d_{T}^{2}}} \right)} - {\frac{1}{R}{mnd}_{R}d_{T}\cos \; {\theta_{r}.}}}$

In this case, the channel matrix can be expressed as

$H = {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi \; R}{\lambda}} \right)}{A\left( \frac{d_{R}^{2}}{\lambda \; R} \right)}{F\left( \frac{d_{T}d_{R}\cos \; \theta_{r}}{\lambda \; R} \right)}{B\left( \frac{d_{T}^{2}}{\lambda \; R} \right)}}$

It can be noted that in this case, the channel matrix can be fullycharacterized, within a complex multiple constant, from the followingthree parameters

$\begin{matrix}{\frac{d_{R}^{2}}{\lambda \; R},\frac{d_{T}d_{R}\cos \; \theta_{r}}{\lambda \; R},{{and}\mspace{14mu} \frac{d_{T}^{2}}{\lambda \; R}},} & \;\end{matrix}$

regardless of the size of the channel matrix (i.e., regardless of thenumber of antennas). Although only three parameters may be required asin the previous case, one of the parameters can be slightly changed. Asa result, the three parameters can now be decoupled in that twoparameters may not be used to compute the third. However, thetransmitter may only need to know two of the three parameters, and thiscan be as in the previous case. Also, as in the previous case, thereceiver can solve for the three parameters from the measured channelmatrix H.

For the completely general case, the distance between the elements ofthe first and second arrays is given by

$r_{m,n} \approx {R + {\frac{1}{2R}m^{2}{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}} + {\frac{1}{2R}n^{2}d_{T}^{2}\cos^{2}\theta_{t}} - {\frac{1}{R}{mnd}_{R}d_{T}\cos \; \theta_{r}\cos \; \theta_{t}} + {{md}_{R}\sin \; \theta_{r}\cos \; \varphi_{r}} - {{nd}_{T}\sin \; {\theta_{t}.}}}$

where ϕ_(r) can be an angle of azimuth of the receiver array ofantennas. In this case, the channel matrix can be expressed as

$H = {\frac{\lambda}{4\; \pi \; R}{\exp \left( {{- j}\frac{2\; \pi \; R}{\lambda}} \right)}{C\left( \frac{d_{R}\sin \; \theta_{r}\cos \; \varphi_{r}}{\lambda} \right)}{{A\left( \frac{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}{\lambda \; R} \right)} \cdot {\quad{{F\left( \frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R} \right)}{B\left( \frac{d_{T}^{2}\cos^{2}\theta_{t}}{\lambda \; R} \right)}{{D\left( \frac{{- d_{T}}\sin \; \theta_{t}}{\lambda} \right)}.}}}}}$

For this case, the situation may be a bit more complicated. The channelmatrix can now be of the form C×A×F×B×D. Here, C, A, B, and D can be alldiagonal matrices. As above the matrix F can be an IDFT matrix which canbe possibly oversampled. For this last case, there can be fiveparameters and each matrix can depend on one of these parameters. Thetransmitter can depend on three of the parameters, whereas in theprevious cases the transmitter may only depend on two parameters. Thereceiver can solve for the five parameters from the measured channelmatrix.

As before, the matrix F is a square IDFT matrix which may beunder-sampled or over-sampled. The matrix C is a diagonal matrix forwhich all non-zero elements have unit magnitude and are given by

C _(i,j)(y)=exp(−jπiy).

Similarly, D is defined as

D _(i,j)(y)=exp(−jπiy)

It can be observed that in the most general case, the channel matrix canbe fully characterized, within a complex multiplicative constant, by thefollowing five parameters

$\frac{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}{\lambda \; R},\frac{d_{R}\sin \; \theta_{r}\cos \; \varphi_{r}}{\lambda},\frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R},\frac{d_{T}^{2}\cos^{2}\theta_{t}}{\lambda \; R},{and}$$\frac{d_{T}\sin \; \theta_{t}}{\lambda}$

regardless of the size of the channel matrix (i.e., regardless of thenumber of antennas). It can also be noted, that in the extreme farfield, we have the following limiting behavior

${\frac{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}{\lambda \; R}\underset{R\rightarrow\infty}{}0},{\frac{d_{T}^{2}\cos^{2}\theta_{t}}{\lambda \; R}\underset{R\rightarrow\infty}{}0}$${\frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R}\underset{R\rightarrow\infty}{}0},$

so that in the extreme far field, only the following terms are non-zero,and these determine the extreme far-field line-of-sight channel

$\frac{d_{R}\sin \; \theta_{r}\cos \; \varphi_{r}}{\lambda},{\frac{d_{T}\sin \; \theta_{t}}{\lambda}.}$

It can be noted that the extreme far-field line-of-sight channel hasrank one and so is also referred to here as the rank one line-of-sightchannel.

As before, let U and V denote the left and right singular vectors of F,respectively. In this case, the left and right singular vectors of theproduct

${C\left( \frac{d_{R}\sin \; \theta_{r}\cos \; \varphi_{r}}{\lambda} \right)}{{A\left( \frac{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}{\lambda \; R} \right)} \cdot {F\left( \frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R} \right)}}{B\left( \frac{d_{T}^{2}\cos^{2}\theta_{t}}{\lambda \; R} \right)}{D\left( \frac{{- d_{T}}\sin \; \theta_{t}}{\lambda} \right)}$

are given by are given by the columns of Ũ and {tilde over (V)},respectively, where

${\overset{\sim}{U} = {{C\left( \frac{d_{R}\sin \; \theta_{r}\cos \; \varphi_{r}}{\lambda} \right)}{A\left( \frac{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}{\lambda \; R} \right)}U}},\text{}{\overset{\sim}{V} = {{B\left( \frac{{- d_{T}^{2}}\cos^{2}\theta_{t}}{\lambda \; R} \right)}{D\left( \frac{d_{T}\sin \; \theta_{t}}{\lambda} \right)}{V.}}}$

Also, the singular values of the product

${C\left( \frac{d_{R}\sin \; \theta_{r}\cos \; \varphi_{r}}{\lambda} \right)}{{A\left( \frac{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}{\lambda \; R} \right)} \cdot {F\left( \frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R} \right)}}{B\left( \frac{d_{T}^{2}\cos^{2}\theta_{t}}{\lambda \; R} \right)}{D\left( \frac{{- d_{T}}\sin \; \theta_{t}}{\lambda} \right)}$

are equal to the singular values of

$F\left( \frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R} \right)$

and thus the singular values only depend on the single parameter

$\frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R}.$

As in the simpler case considered previously, it is possible to estimatethe five parameters that completely determine the LOS channel (within acomplex scalar) from measurements of the channel, though the problem isslightly more complicated. Let the K×L matrix Ĥ denote the channelmeasured using reference symbols, which is given by

Ĥ=H+N

and N is a K×L matrix of i.i.d. complex Gaussian random variables ofvariance σ². Let the K×L matrix ∠Ĥ denote phases of the elements of Ĥmeasured in radians. Let the (K−1)×L matrix Δ_(R)(∠Ĥ) denote the matrixwith k-th row equal to the result of subtracting the k-th row of ∠Ĥ fromthe k+1-th row of ∠Ĥ. The matrix Δ_(R)(∠Ĥ) can also be computed bydividing the k+1-th row of Ĥ by the k-th row of Ĥ and taking the phaseof each element of the resulting (K−1)×L matrix. The matrix Δ_(R)(∠Ĥ)can be written in the form

${\Delta_{R}\left( {\angle \; \hat{H}} \right)} = {{{- \pi} \cdot \begin{bmatrix}{a + b} & {a + b - {2c}} & \ldots & {a + b - {2\left( {L - 1} \right)c}} \\{{3a} + b} & {{3a} + b - {2c}} & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots \\{{\left( {{2K} - 1} \right)a} + b} & \ldots & \ldots & {{\left( {{2K} - 1} \right)a} + b - {2\left( {L - 1} \right)c}}\end{bmatrix}} + N_{R}}$

where the K−1×L matrix N_(R) denotes the noise in the calculation of thephase differences between rows, and a, b and c denote the parameters

${a = \frac{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}{\lambda \; R}},{b = \frac{d_{R}\sin \; \theta_{r}\cos \; \varphi_{r}}{\lambda}},{and}$$c = \frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R}$

Let Δ_(R) ^(S)(∠Ĥ) denote the stacked columns of Δ_(R)(∠Ĥ), and letN_(R) ^(S) denote the stacked columns of N_(∠). We then have that

${\Delta_{R}^{s}\left( {\angle \; \hat{H}} \right)} = {{{- {{\pi \begin{bmatrix}1 & 1 & 0 \\3 & 1 & 0 \\\vdots & \vdots & \vdots \\{{2K} - 1} & 1 & 0 \\1 & 1 & {- 2} \\3 & 1 & {- 2} \\\vdots & \vdots & \vdots \\{{2K} - 1} & 1 & {- 2} \\\vdots & \vdots & \vdots \\\vdots & \vdots & \vdots \\\vdots & \vdots & \vdots \\\vdots & \vdots & \vdots \\1 & 1 & {{- 2}\left( {L - 1} \right)} \\3 & 1 & {{- 2}\left( {L - 1} \right)} \\\vdots & \vdots & \vdots \\{{2K} - 1} & 1 & {{- 2}\left( {L - 1} \right)}\end{bmatrix}}\begin{bmatrix}a \\b \\c\end{bmatrix}}} + N_{R}^{S}} = {{W_{R}\begin{bmatrix}a \\b \\c\end{bmatrix}} + N_{R}^{S}}}$

where the (K−1)L×3 matrix W_(R) is implicitly defined from the aboveequation.

This system of equation is highly over-determined since we have (K−1)Lequations with only three unknowns. With the formulation, theleast-squared error estimate is given by

$\begin{bmatrix}\frac{d_{R}^{2}\left( {1 - {\sin^{2}\theta_{r}\cos^{2}\varphi_{r}}} \right)}{\lambda \; R} \\\frac{d_{R}\sin \; \theta_{r}\cos \; \varphi_{r}}{\lambda} \\\frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R}\end{bmatrix}_{LSE} = {\left( {W_{R}^{H}W_{R}} \right)^{- 1}W_{R}^{H}{\Delta_{R}^{s}\left( {\angle \; \hat{H}} \right)}}$

Similarly, to solve for the last two parameters, let the matrix K×(L−1)matrix Δ_(C)(∠Ĥ) denote the matrix with k-th row equal to the result ofsubtracting the l-th column of ∠Ĥ from the l+1-th column of ∠Ĥ. Thematrix Δ_(C)(∠Ĥ) can also be computed by dividing the l+1-th column of Ĥby the l-th column of Ĥ and taking the phase of each element of theresulting K×(L−1) matrix. The matrix Δ_(C)(∠Ĥ) is given by

${\Delta_{C}\left( {\angle \; \hat{H}} \right)} = {{- {\pi \begin{bmatrix}{e - d - {2c}} & {{3e} - d - {2c}} & \ldots & {{\left( {{2L} - 1} \right)e} - d - {2c}} \\{e - d - {4c}} & {{3e} - d - {4c}} & \ldots & \ldots \\\ldots & \ldots & \ldots & \ldots \\{e - d - {2{Kc}}} & \ldots & \ldots & {{\left( {{2L} - 1} \right)e} - d - {2{Kc}}}\end{bmatrix}}} + N_{C}}$

where the K−1×L matrix N_(C) denotes the noise in the calculation of thephase differences between columns, and c, d and e denote the parameters

${c = \frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R}},{d = \frac{d_{T}\sin \; \theta_{t}}{\lambda \;}},{{{and}\mspace{14mu} e} = {\frac{d_{T}^{2}{\cos \;}^{2}\theta_{t}}{\lambda \; R}.}}$

Let Δ_(C) ^(S)(∠Ĥ) denote the stacked columns of Δ_(C)(∠Ĥ), and letN_(C) ^(S) denote the stacked columns of N_(C). We then have that

${\Delta_{C}^{s}\left( {\angle \; \hat{H}} \right)} = {{{- {{\pi \begin{bmatrix}1 & {- 1} & {- 2} \\1 & {- 1} & {- 4} \\\vdots & \vdots & \vdots \\1 & {- 1} & {{- 2}K} \\3 & {- 1} & {- 2} \\3 & {- 1} & {- 4} \\\vdots & \vdots & \vdots \\3 & {- 1} & {{- 2}K} \\\vdots & \vdots & \vdots \\\vdots & \vdots & \vdots \\\vdots & \vdots & \vdots \\\vdots & \vdots & \vdots \\{{2L} - 1} & {- 1} & {- 2} \\{{2L} - 1} & {- 1} & {- 4} \\\vdots & \vdots & \vdots \\{{2L} - 1} & {- 1} & {{- 2}K}\end{bmatrix}}\begin{bmatrix}c \\d \\e\end{bmatrix}}} + N_{C}^{S}} = {{W_{C}\begin{bmatrix}c \\d \\e\end{bmatrix}} + {N_{C}^{S}.}}}$

where the K(L−1)×3 matrix W_(C) is implicitly defined from the aboveequation. This system of equation is highly over-determined since wehave (K−1)L equations with only three unknowns. With the formulation,the least-squared estimate is given by

$\begin{bmatrix}\frac{d_{T}^{2}\cos^{2}\theta_{t}}{\lambda \; R} \\\frac{d_{T}\sin \; \theta_{t}}{\lambda} \\\frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R}\end{bmatrix}_{LSE} = {\left( {W_{C}^{H}W_{C}} \right)^{- 1}W_{C}^{H}{{\Delta_{C}^{s}\left( {\angle \; \hat{H}} \right)}.}}$

FIG. 4 is an example flowchart 400 illustrating the operation of adevice, such as the receiver 120, according to a possible embodiment.For example, the method can be performed at a UE, an eNB, and/or anyother device that can receive reference signals and measure a channelmatrix. At 410, reference signals from a transmitting device can bereceived at a receiving device. At 420, a channel matrix H can bemeasured based on the reference signals.

At 430, at least two of a first line of sight channel parameter, asecond line of sight channel parameter, and a third line of sightchannel parameter can be extracted based on the channel matrix H. Thefirst line of sight channel parameter can be based on transmittingdevice antenna element spacing. The second line of sight channelparameter can be based on a product of the transmitting device antennaelement spacing and a receiving device antenna element spacing. Thethird line of sight channel parameter can be based on the receivingdevice antenna element spacing. The parameters can be extracted byforming a least-squared error estimate of the at least two line of sightchannel parameters based on the channel matrix H. For example, withadditive noise, a least-squares and/or iterative formulation can be usedto solve for these parameters.

At least one of the at least two line of sight channel parameters can bebased on a link range (R) between antennas at a transmitting device andantennas at a receiving device, a distance (d_(T)) between neighboringtransmit antennas, a distance (d_(R)) between neighboring receiveantennas, and a wavelength (λ₁) of a carrier signal of the referencesignals. For example, one or both of the at least two line of sightchannel parameters can be based on the link range, the distances betweenantennas, and the wavelength when antenna arrays at the transmittingdevice and the receiving device are parallel and planes perpendicular toa line connecting the endpoints of the two arrays.

The first line of sight parameter can be a two-dimension parameter basedon the transmitting device antenna element spacing in a horizontaldirection and the transmitting device antenna element spacing in avertical dimension. The third line of sight parameter can be atwo-dimension parameter based on the receiving device antenna elementspacing in the horizontal and receiving device antenna element spacingin the vertical dimension. For example, the transmitting antennas can beseparated in two dimensions and receiving antennas can be separated intwo dimensions.

The channel matrix H can be equal to a complex number multiplied bythree matrices A, F, and B, where A and B can be diagonal matrices andwhere F can be an Inverse Discrete Fourier Transform (IDFT) matrix or anoversampled IDFT matrix. Elements of the matrix A can be based on thefirst line of sight channel parameter. Elements of the matrix F can bebased on the second line of sight channel parameter. Elements of thematrix B can be based on the third line of sight channel parameter.

The channel matrix H can also be equal to a complex number multiplied byfive matrices C, A, F, B and D, where C, A, B and D can be diagonalmatrices, and F can be an IDFT matrix or an oversampled IDFT matrix. Inother words, the channel matrix H can be equal to a complex numbermultiplied by three matrices A′, F, and B′, where A′ can be A×C, B′ canbe B×D, and all the multiplicand matrices can be diagonal matrices. Thematrices C and D each can have a parameter associated with them that isdependent on the geometry. The diagonal elements of A all can have equalamplitude (typically one). Similarly, the diagonal elements of each ofB, C, and D all can have equal amplitude (typically one).

The channel matrix H can also be equal to a Kronecker product of ahorizontal antenna channel matrix H_(h) and a vertical antenna channelmatrix H_(v). The horizontal antenna channel matrix H_(h) can be equalto a complex number multiplied by three matrices A_(h), F_(h), andB_(h), where A_(h) and B_(h) can be diagonal matrices and F_(h) can bean IDFT matrix or an oversampled IDFT matrix. The diagonal elements ofA_(h) all can have equal amplitude (typically one) and the diagonalelements of B_(h) all can have equal amplitude. The vertical antennachannel matrix H_(v) can be equal to a complex number multiplied bythree matrices A_(v), F_(v), and B_(v), where A_(v) and B_(v) can bediagonal matrices and F_(v) can be an IDFT matrix or an oversampled IDFTmatrix.

At 440, the line of site parameters can be utilized. For example,according to a possible implementation, precoders can be determinedbased on the at least two line of sight channel parameters and theprecoders can be applied to an antenna array. The receiving device canapply the precoders to the channel to determine a Channel QualityIndicator (CQI). The receiving device can also apply the precoders totransmitted signals. The transmitting device can also determine theprecoders based on the at least two line of sight channel parameters.

According to another possible related implementation, a rotation of anantenna array at the receiving device can be adjusted based on at leastone of the line of sight channel parameters. For example, the rotationof the antenna array can be adjusted to improve the spacing of theelements relative to the orientation of the transmitter and receiver.The rotation of the antenna array can also be adjusted at thetransmitting device. Alternatively, the transmitter and/or receiver canchange the subset of antenna elements (from a presumed larger array)that are used to transmit and/or receive.

According to another possible related implementation, at least one ofthe line of sight channel parameters can be evaluated over a set ofallowed wavelengths. A wavelength that yields the channel matrix H withthe largest capacity can be selected from the set of allowedwavelengths.

According to another possible related implementation, an invertedchannel mode of transmission can be selected based on a line of sightchannel parameter being approximately equal to a reciprocal of a numberof antennas in an array of antennas of the transmitting device. Fullrank transmission can be when the transmission rank or number of layersequals the number of transmit antennas, where the transmission rank canbe the number of transmission streams transmitted simultaneously on asame frequency resource. For example, full rank can be a number oflayers that are the minimum of the number M of transmit antennas and thenumber N of receive antennas, such as the minimum of M and N. As afurther example, a simplified receiver can be enabled by inverting thechannel matrix H prior to transmission by first multiplying the datavector by a diagonal matrix, taking the DFT of the pre-multiplied datavector, and finally by multiplying the output of the DFT by anotherdiagonal matrix. In this case, a simplified receiver can be a MIMOreceiver in which the data estimate can be formed by simply multiplyingthe vector output of the receive antenna array by a complex scalar.Conversely, in a typical MIMO receiver, the data estimate can be formedby multiplying the vector output of the receive antenna array by acomplex-valued matrix. For a DFT taken of data for transmission at thetransmitter, if it is assumed that both the transmit and receive antennaarrays have M antennas, then a vector of M data symbols can be presentedto the transmitter. The transmitter can first multiply the data vectorby a diagonal matrix, take the DFT of the pre-multiplied data vector,multiply the output of the DFT by another diagonal matrix. The outputcan be another vector of M symbols. Each of these M symbols can then bemapped, in order, to the M elements of the antenna array.

According to another possible related implementation, the at least twoline of sight channel parameters can be scaled by a ratio of awavelength (λ₁) of a carrier signal of the reference signals to atransmit wavelength. According to another possible relatedimplementation, a subset of transmitting device antennas that yieldimproved line of sight capacity over a set of transmitting deviceantennas can be determined based on at least one of the at least twoline of sight channel parameters. For example, a receiver UE candetermine the subset of L transmitter eNB or Access Point (AP) antennasthat yields the best LOS capacity and signal this set back to the eNB orAP. This subset of antennas may be regularly spaced.

At 450, the at least two line of sight channel parameters can betransmitted to the transmitting device. Transmitting can includetransmitting the scaled at least two line of sight channel parameters tothe transmitting device. Also, the subset of transmitting deviceantennas can be signaled to the transmitting device. Additionally, ascaling factor for the channel matrix H can be signaled to thetransmitting device. For example, the scaling factor can be based on

$\frac{\lambda}{4\pi \; R}{\exp \left( {{- j}\; \frac{2\pi \; R}{\lambda}} \right)}$

and the signaled scaling factor can be the amplitude:

$\frac{\lambda}{4\pi \; R}.$

The scaling factor can be used for the spacing that optimizes thecapacity of a communication link and can be used to determine a codingrate that can be used at the transmitting device.

FIG. 5 is an example flowchart 500 illustrating the operation of adevice, such as the transmitter 110, according to a possible embodiment.At 510, reference symbols can be transmitted from a regularly spacedsubset of a set of transmitting device antenna elements of a transmitterwith locations in one or more spatial dimensions. The regularly spacedsubset of the transmitting device antenna elements can be generated by acombination of a subset from the antenna elements of a horizontaldimension antenna array and a subset from the antenna elements of avertical dimension antenna array. At 520, transmit antenna elementspacings in each dimension can be signaled, where the transmit antennaelement spacings can be used by the transmitter for data transmission.The transmit antenna element spacings can be signaled in the form ofratios to the spacing of transmitting device antenna elements that wereused for the transmitted references symbols.

At 530, a line of sight channel parameter can be received. The line ofsight channel parameter can be

$\frac{d_{T}d_{R}}{\lambda_{1}R}$

where R can be link range between antennas at a transmitting device andantennas at a receiving device, d_(T) can be a distance betweenneighboring transmit antennas, d_(R) can be a distance betweenneighboring receive antennas, and λ₁ can be a wavelength of a carriersignal.

The line of sight channel parameter can also be

$\frac{d_{T}d_{R}\cos \; \theta_{r}}{\lambda \; R}$

where θ_(r) can be an angle of declination angle of the receiver arrayof antennas. For example, the line of sight parameter can be multipliedby an additional factor that is geometry dependent.

The line of sight channel parameter can also be

$\frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R}$

where θ_(t) can be an angle of declination angle of an array of thetransmitting device antenna elements.

An additional line of sight channel parameter that includes a scalingfactor for the line of sight channel can also be received. The scalingfactor can scale a channel matrix H in order to determine the codingrate that can be used at the transmitter.

At 540, transmit antenna element spacings in each spatial dimension canbe selected that maximize a communication link capacity based on theline of sight channel parameter. The assumption here can be that thetotal number of antenna elements used for transmission is same so thattotal power is also same.

At 550, a number of antenna elements for transmission in each dimensioncan be generated based on the selected transmit antenna elementspacings. A product of the number of antenna elements in each dimensionis less than a predefined value. This can ensure that the total power isbelow a threshold. Transmissions can then be made using the number ofantenna elements.

FIG. 6 is an example flowchart 600 illustrating the operation of adevice, such as the receiver 120, according to a possible embodiment. At610, reference signals can be received from a transmitting device. At620, element spacings can be received. The element spacings can be foreach spatial dimension of an array of antennas at the transmittingdevice. The element spacings can be allowed element spacings. At 630, achannel matrix H(λ₁) based on the reference signals can be measured. At640, a line of sight channel parameter for each element spacing for eachspatial dimension of the array of antennas at the transmitting devicecan be extracted based on the channel matrix H(λ₁).

At 650, the spacing for antennas in the array of antennas in eachspatial dimension that optimizes a capacity of a communication link canbe determined based on the line of sight channel parameter. At 660, aspacing for antennas in the array of antennas in each spatial dimensionthat optimizes a capacity of a communication link can be selected. At670, the spacing that optimizes the capacity of the communication linkcan be signaled, such as to the transmitting device. A scaling factorfor the matrix H(λ₁) for the spacing that optimizes the capacity of acommunication link can also be signaled. For example, the scaling factorcan be based on

$\frac{\lambda}{4\pi \; R}{\exp \left( {{- j}\; \frac{2\pi \; R}{\lambda}} \right)}$

and the signaled scaling factor can be the amplitude:

$\frac{\lambda}{4\pi \; R}.$

FIG. 7 is an example flowchart 700 illustrating the operation of adevice, such as the receiver 120, according to a possible embodiment. At710, reference signals can be received. At 720, a channel matrix H(λ₁)can be measured based on the reference signals. At 730, a least-squarederror estimate of the measured channel matrix H(λ₁) can be determined.At 740, a sum-squared error can be calculated based on the least-squarederror estimate. At 750, the sum-squared error based on the least-squarederror estimate can be compared to a threshold.

At 760, the measured channel matrix H(λ₁) can be ascertained to beclassified as a LOS-MIMO channel based on comparing the sum-squarederror based on the least-squared error estimate to the threshold. Themeasured channel matrix H(λ₁) can also be ascertained to be classifiedas a rank one LOS channel based on comparing a sum-squared error basedon the least-squared error estimate to a threshold. The transmissionrank can be the number of transmission streams transmittedsimultaneously on a same frequency resource. For example, the measuredchannel matrix H(λ₁) can be ascertained to be classified as a rank oneLOS channel based on comparing a sum-squared error based on theleast-squared error estimate to a threshold. Then a phase difference ofreference signals received at a single receive antenna and transmittedfrom two different antennas can be measured.

At 770, a line of sight channel parameter can be extracting based on thechannel matrix H(λ₁). The line of sight channel parameter can beextracted by calculating a phase angle based on an estimate of thechannel matrix. The line of sight channel parameter can also beextracted by calculating the phase angle of a ratio of two adjoiningelements of the estimate of the channel matrix. The line of sightchannel parameter can also be extracted by an optimization of an errorvalue of the calculated phase angle. The optimization of the error valueof the calculated phase angle can be performed by a least-squared errormethod.

The line of sight channel parameter can be

$\frac{d_{T}d_{R}}{\lambda_{1}R}$

where R can be link range between antennas at a transmitting device andantennas at a receiving device, d_(T) can be a distance betweenneighboring transmit antennas, d_(R) can be a distance betweenneighboring receive antennas, and λ₁ can be a wavelength of a carriersignal.

The line of sight channel parameter can also be

$\frac{d_{T}d_{R}\cos \; \theta_{r}}{\lambda \; R}$

where θ_(r) can be an angle of declination angle of the receiver arrayof antennas. For example, the line of sight parameter can be multipliedby an additional factor that is geometry dependent.

The line of sight channel parameter can additionally be

$\frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R}$

where θ_(t) can be an angle of declination angle of an array of thetransmitting device antenna elements.

At 780, an indication that the measured channel matrix H(λ₁) isclassified as a LOS-MIMO channel can be transmitted based on comparing asum-squared error based on the least-squared error estimate to athreshold. The line of sight parameter can also be transmitted. Anindication of the measured phase difference of the reference signals canadditionally be signaled to the transmitting device. A scaling factorcan also be signaled for the channel matrix H(λ). For example, thescaling factor can be based on

$\frac{\lambda}{4\pi \; R}{\exp \left( {{- j}\; \frac{2\pi \; R}{\lambda}} \right)}$

and the signaled scaling factor can be the amplitude

$\frac{\lambda}{4\pi \; R}.$

The scaling factor can be used to determine a coding rate that can beused at the transmitting device.

FIG. 8 is an example flowchart 800 illustrating the operation of adevice, such as the transmitter 110, according to a possible embodiment.At 810, reference signals can be transmitted from two differenttransmitter antennas. At 820, an indication can be received thatindicates a channel matrix H(λ₁) is classified as a rank one LOSchannel. At 830, an indication of a phase difference of the referencesignals transmitted from the two different transmitter antennas to asingle receive antenna can be received.

At 840, a line of sight channel parameter can be received. The line ofsight channel parameter can be

$\frac{d_{T}d_{R}}{\lambda_{1}R}$

where R can be a link range between antennas at a transmitting deviceand antennas at a receiving device, d_(T) can be a distance betweenneighboring transmit antennas, d_(R) can be a distance betweenneighboring receive antennas, and λ₁ can be a wavelength of a carriersignal.

The line of sight channel parameter can also be

$\frac{d_{T}d_{R}\cos \; \theta_{r}}{\lambda \; R}$

where θ_(r) can be an angle of declination angle of the receiver arrayof antennas. For example, the line of sight parameter can be multipliedby an additional factor that is geometry dependent.

The line of sight channel parameter can additionally be

$\frac{d_{T}d_{R}\cos \; \theta_{r}\cos \; \theta_{t}}{\lambda \; R}$

where θ_(t) can be an angle of declination angle of an array of thetransmitting device antenna elements.

At 850, antenna element spacing in each spatial dimension can beselected that maximizes a communication link capacity based on the atleast one line of sight channel parameter. At 860, signals from twotransmit antennas can be co-phased by the received indicated phasedifference so they arrive in-phase at a receiving device.

It should be understood that, notwithstanding the particular steps asshown in the figures, a variety of additional or different steps can beperformed depending upon the embodiment, and one or more of theparticular steps can be rearranged, repeated or eliminated entirelydepending upon the embodiment. Also, some of the steps performed can berepeated on an ongoing or continuous basis simultaneously while othersteps are performed. Furthermore, different steps can be performed bydifferent elements or in a single element of the disclosed embodiments.

FIG. 9 is an example block diagram of an apparatus 900, such as thetransmitter 110 or the receiver 120, according to a possible embodiment.The apparatus 900 can include a housing 910, a controller 920 within thehousing 910, audio input and output circuitry 930 coupled to thecontroller 920, a display 940 coupled to the controller 920, atransceiver 950 coupled to the controller 920, a user interface 960coupled to the controller 920, a memory 970 coupled to the controller920, and a network interface 980 coupled to the controller 920. Theapparatus 900 can also include a plurality of antennas, such as anantenna array, including at least antennas 952 and antenna 954 coupledto the transceiver 950. The transceiver 950 can be one or a plurality oftransceivers. The apparatus 900 can perform the methods described in allthe embodiments.

The display 940 can be a viewfinder, a liquid crystal display (LCD), alight emitting diode (LED) display, a plasma display, a projectiondisplay, a touch screen, or any other device that displays information.The transceiver 950 can include a transmitter and/or a receiver. Theaudio input and output circuitry 930 can include a microphone, aspeaker, a transducer, or any other audio input and output circuitry.The user interface 960 can include a keypad, a keyboard, buttons, atouch pad, a joystick, a touch screen display, another additionaldisplay, or any other device useful for providing an interface between auser and an electronic device. The network interface 980 can be aUniversal Serial Bus (USB) port, an Ethernet port, an infraredtransmitter/receiver, an IEEE 1394 port, a WLAN transceiver, or anyother interface that can connect an apparatus to a network, device, orcomputer and that can transmit and receive data communication signals.The memory 970 can include a random access memory, a read only memory,an optical memory, a flash memory, a removable memory, a hard drive, acache, or any other memory that can be coupled to an apparatus.

The apparatus 900 or the controller 920 may implement any operatingsystem, such as Microsoft Windows®, UNIX®, or LINUX®, Android™, or anyother operating system. Apparatus operation software may be written inany programming language, such as C, C++, Java or Visual Basic, forexample. Apparatus software may also run on an application framework,such as, for example, a Java® framework, a .NET® framework, or any otherapplication framework. The software and/or the operating system may bestored in the memory 970 or elsewhere on the apparatus 900. Theapparatus 900 or the controller 920 may also use hardware to implementdisclosed operations. For example, the controller 920 may be anyprogrammable processor. Disclosed embodiments may also be implemented ona general-purpose or a special purpose computer, a programmedmicroprocessor or microprocessor, peripheral integrated circuitelements, an application-specific integrated circuit or other integratedcircuits, hardware/electronic logic circuits, such as a discrete elementcircuit, a programmable logic device, such as a programmable logicarray, field programmable gate-array, or the like. In general, thecontroller 920 may be any controller or processor device or devicescapable of operating an apparatus and implementing the disclosedembodiments.

According to a possible embodiment, the transceiver 950 can receivereference signals as a receiving device from a transmitting device. Thecontroller 920 can measure a channel matrix H(λ₁) based on the referencesignals. The channel matrix H(λ₁) can be equal to a complex numbermultiplied by three matrices A, F, and B, where A and B can be diagonalmatrices and F can be an Inverse Discrete Fourier Transform (IDFT)matrix or an oversampled IDFT matrix.

The controller 920 can extract, based on the channel matrix H(λ₁), atleast two of a first line of sight channel parameter, a second line ofsight channel parameter, and a third line of sight channel parameter,where the first line of sight channel parameter can be based ontransmitting device antenna element spacing, where the second line ofsight channel parameter can be based on a product of the transmittingdevice antenna element spacing and antenna element spacing of theantenna array 952 and 954, and where the third line of sight channelparameter can be based on the antenna element spacing of the antennaarray 952 and 954. The controller 920 can perform the extraction byforming a least-squared error estimate of the at least two line of sightchannel parameters based on the channel matrix H(λ₁).

According to a possible implementation, the controller 920 can determineprecoders based on the at least two line of sight channel parameters andapply the precoders to the antenna array 952 and 954. According toanother related possible implementation, the controller 920 can adjust arotation of the antenna array 952 and 954 based on at least one of theline of sight channel parameters. According to another related possibleimplementation, the controller 920 can determine a subset oftransmitting device antennas that yield improved line of sight capacityover a set of transmitting device antennas based on at least one of theat least two line of sight channel parameters, and can signal the subsetof transmitting device antennas to the transmitting device. According toanother related possible implementation, the controller 920 can evaluateat least one of the line of sight channel parameters over a set ofallowed wavelengths and can select a wavelength from the set of allowedwavelengths that yields the channel matrix H(λ₁) with the largestcapacity. According to another related possible implementation, thecontroller 920 can select an inverted channel mode of transmission basedon a line of sight channel parameter being approximately equal to areciprocal of a number of antennas in an array of antennas of thetransmitting device. The transceiver 950 can transmit the at least twoline of sight channel parameters to the transmitting device.

According to another possible embodiment, the transceiver 950 cantransmit reference symbols from a regularly spaced subset of a set ofantenna elements with locations in one or more spatial dimensions. Theregularly spaced subset of the antenna elements can be generated by acombination of a subset from the antenna elements of a horizontaldimension antenna array and a subset from the antenna elements of avertical dimension antenna array. The transceiver 950 can signaltransmit antenna element spacings in each dimension that can be used bythe transceiver 950 for data transmission. The transmit antenna elementspacings can be signaled in the form of ratios to the spacing of antennaelements that were used for the transmitted references symbols.

The transceiver 950 can receive a line of sight channel parameter. Thecontroller 920 can select the transmit antenna element spacings in eachspatial dimension that maximize a communication link capacity based onthe line of sight channel parameter. The transceiver 950 can alsoreceive an additional line of sight channel parameter that includes ascaling factor for the line of sight channel. The controller 920 candetermine a number of antenna elements for transmission in eachdimension based on the transmit antenna element spacings. A product ofthe number of antenna elements in each dimension can be less than apredefined value.

According to another possible embodiment, the transceiver 950 canreceive reference signals from a transmitting device. The transceiver950 can receive element spacings for each spatial dimension of an arrayof antennas at the transmitting device. The controller 920 can measure achannel matrix H(λ₁) based on the reference signals. The controller 920can extract, based on the channel matrix H(λ₁), a line of sight channelparameter for each element spacing for each spatial dimension of thearray of antennas at the transmitting device. The controller 920 canselect a spacing for antennas in the array of antennas at thetransmitting device in each spatial dimension that optimizes a capacityof a communication link. The transceiver 950 can signal the spacing thatoptimizes the capacity of the communication link.

According to another possible embodiment, a transceiver 950 can receivereference signals. The controller 920 can measure a channel matrix H(λ₁)based on the reference signals. The controller 920 can determine aleast-squared error estimate of the measured channel matrix H(λ₁). Thecontroller 920 can calculate a sum-squared error based on theleast-squared error estimate. The controller 920 can compare thesum-squared error based on the least-squared error estimate to athreshold. The controller 920 can ascertain the measured channel matrixH(λ₁) is classified as a LOS-MIMO channel based on comparing thesum-squared error based on the least-squared error estimate to thethreshold.

The transceiver 950 can transmit an indication that the measured channelmatrix H(λ₁) is classified as a LOS-MIMO channel based on comparing asum-squared error based on the least-squared error estimate to athreshold. The controller 920 can extract a line of sight channelparameter based on the channel matrix H(λ₁) and the transceiver 950 cantransmit the line of sight channel parameter.

The controller 920 can also ascertain the measured channel matrix H(λ₁)is classified as a rank one LOS channel based on comparing a sum-squarederror based on the least-squared error estimate to a threshold. Thecontroller 920 can additionally measure a phase difference of referencesignals received at a single receive antenna and transmitted from twodifferent antennas. The transceiver can signal an indication of thephase difference to the transmitting device.

According to another possible embodiment, the transceiver 950 cantransmit reference signals from two of a plurality of antennas. Thetransceiver 950 can receive an indication indicating a channel matrixH(λ₁) is classified as a rank one LOS channel. The transceiver 950 canreceive an indication of a phase difference of reference signalstransmitted from two different antennas of the plurality of antennas toa single receive antenna. The transceiver 950 can receive a line ofsight channel parameter. The controller 920 can select antenna elementspacing in each spatial dimension that maximizes a communication linkcapacity based on the at least one line of sight channel parameter. Thecontroller 920 can co-phase signals from two antennas by the receivedindicated phase difference so they arrive in-phase at a receivingdevice.

The method of this disclosure can be implemented on a programmedprocessor. However, the controllers, flowcharts, and modules may also beimplemented on a general purpose or special purpose computer, aprogrammed microprocessor or microcontroller and peripheral integratedcircuit elements, an integrated circuit, a hardware electronic or logiccircuit such as a discrete element circuit, a programmable logic device,or the like. In general, any device on which resides a finite statemachine capable of implementing the flowcharts shown in the figures maybe used to implement the processor functions of this disclosure.

While this disclosure has been described with specific embodimentsthereof, it is evident that many alternatives, modifications, andvariations will be apparent to those skilled in the art. For example,various components of the embodiments may be interchanged, added, orsubstituted in the other embodiments. Also, all of the elements of eachfigure are not necessary for operation of the disclosed embodiments. Forexample, one of ordinary skill in the art of the disclosed embodimentswould be enabled to make and use the teachings of the disclosure bysimply employing the elements of the independent claims. Accordingly,embodiments of the disclosure as set forth herein are intended to beillustrative, not limiting. Various changes may be made withoutdeparting from the spirit and scope of the disclosure.

In this document, relational terms such as “first,” “second,” and thelike may be used solely to distinguish one entity or action from anotherentity or action without necessarily requiring or implying any actualsuch relationship or order between such entities or actions. The phrase“at least one of” or “at least one selected from the group of” followedby a list is defined to mean one, some, or all, but not necessarily allof, the elements in the list. The terms “comprises,” “comprising,” orany other variation thereof, are intended to cover a non-exclusiveinclusion, such that a process, method, article, or apparatus thatcomprises a list of elements does not include only those elements butmay include other elements not expressly listed or inherent to suchprocess, method, article, or apparatus. An element proceeded by “a,”“an,” or the like does not, without more constraints, preclude theexistence of additional identical elements in the process, method,article, or apparatus that comprises the element. Also, the term“another” is defined as at least a second or more. The terms“including,” “having,” and the like, as used herein, are defined as“comprising.” Furthermore, the background section is written as theinventor's own understanding of the context of some embodiments at thetime of filing and includes the inventor's own recognition of anyproblems with existing technologies and/or problems experienced in theinventor's own work.

We claim:
 1. A method comprising: receiving reference signals at areceiving device from a transmitting device; measuring a channel matrixbased on the reference signals; extracting, based on the channel matrix,at least two of a first line of sight channel parameter, a second lineof sight channel parameter, and a third line of sight channel parameter,where the first line of sight channel parameter is based on transmittingdevice antenna element spacing, where the second line of sight channelparameter is based on a product of the transmitting device antennaelement spacing and a receiving device antenna element spacing, andwhere the third line of sight channel parameter is based on thereceiving device antenna element spacing; and transmitting the at leasttwo line of sight channel parameters to the transmitting device.
 2. Themethod according to claim 1, wherein the channel matrix H is equal to acomplex number multiplied by three matrices A, F, and B, where A and Bare diagonal matrices, and where F is an Inverse Discrete FourierTransform matrix or an oversampled Inverse Discrete Fourier Transformmatrix.
 3. The method according to claim 2, wherein elements of thematrix A are based on the first line of sight channel parameter, whereinelements of the matrix F are based on the second line of sight channelparameter, and wherein elements of the matrix B are based on the thirdline of sight channel parameter.
 4. The method according to claim 1,further comprising: determining precoders based on the at least two lineof sight channel parameters; and applying the precoders to an antennaarray.
 5. The method according to claim 1, wherein extracting comprisesforming a least-squares estimate of the at least two line of sightchannel parameters based on the channel matrix.
 6. The method accordingto claim 1, wherein at least one of the at least two line of sightchannel parameters is based on a link range between antennas at atransmitting device and antennas at a receiving device, a distancebetween neighboring transmit antennas, a distance between neighboringreceive antennas, and a wavelength of a carrier signal of the referencesignals.
 7. The method according to claim 1, further comprisingadjusting a rotation of an antenna array at the receiving device basedon at least one of the line of sight channel parameters.
 8. The methodaccording to claim 1, further comprising: determining a subset oftransmitting device antennas that yield improved line of sight capacityover a set of transmitting device antennas based on at least one of theat least two line of sight channel parameters; and signaling the subsetof transmitting device antennas to the transmitting device.
 9. Themethod according to claim 1, further comprising: evaluating at least oneof the line of sight channel parameters over a set of allowedwavelengths; and selecting a wavelength that yields the channel matrixwith the largest capacity from the set of allowed wavelengths.
 10. Themethod according to claim 1, wherein the method further comprisesscaling the at least two line of sight channel parameters by a ratio ofa wavelength of a carrier signal of the reference signals to a transmitwavelength, AND wherein transmitting comprises transmitting the scaledat least two line of sight channel parameters to the transmittingdevice.
 11. The method according to claim 1, wherein the first line ofsight parameter is a two-dimension parameter based on the transmittingdevice antenna element spacing in a horizontal direction and thetransmitting device antenna element spacing in a vertical dimension. 12.The method according to claim 1, wherein the third line of sightparameter is a two-dimension parameter based on the receiving deviceantenna element spacing in the horizontal and receiving device antennaelement spacing in the vertical dimension.
 13. The method according toclaim 1, wherein the channel matrix is equal to a Kronecker product of ahorizontal antenna channel matrix and a vertical antenna channel matrix.14. The method according to claim 13, wherein the horizontal antennachannel matrix is equal to a complex number multiplied by three matricesA_(h), F_(h), and B_(h), where A_(h) and B_(h) are diagonal matrices,and where F_(h) is an Inverse Discrete Fourier Transform matrix or anoversampled Inverse Discrete Fourier Transform matrix.
 15. The methodaccording to claim 13, wherein the vertical antenna channel matrix isequal to a complex number multiplied by three matrices A_(v), F_(v), andB_(v), where A_(v) and B_(v) are diagonal matrices, and where F_(v) isan Inverse Discrete Fourier Transform matrix or an oversampled InverseDiscrete Fourier Transform matrix.
 16. The method according to claim 1,further comprising selecting an inverted channel mode of transmissionbased on a line of sight channel parameter being approximately equal toa reciprocal of a number of antennas in an array of antennas of thetransmitting device.
 17. The method according to claim 1, wherein thechannel matrix is equal to a complex number multiplied by five matricesC, A, F, B and D, where C, A, B and D are diagonal matrices, and where Fis an Inverse Discrete Fourier Transform matrix or an oversampledInverse Discrete Fourier Transform matrix.
 18. The method according toclaim 1, further comprising signaling a scaling factor for the channelmatrix.
 19. An apparatus comprising: an antenna array including aplurality of antenna elements; a transceiver coupled to the array ofantennas, the transceiver to receive reference signals from atransmitting device; and a controller to measure a channel matrix basedon the reference signals, and extract, based on the channel matrix, atleast two of a first line of sight channel parameter, a second line ofsight channel parameter, and a third line of sight channel parameter,where the first line of sight channel parameter is based on transmittingdevice antenna element spacing, where the second line of sight channelparameter is based on a product of the transmitting device antennaelement spacing and an antenna element spacing of the antenna array, andwhere the third line of sight channel parameter is based on the antennaelement spacing of the antenna array, wherein the transceiver transmitsthe at least two line of sight channel parameters to the transmittingdevice.
 20. The apparatus according to claim 19, wherein the channelmatrix is equal to a complex number multiplied by three matrices A, F,and B, where A and B are diagonal matrices, and where F is an InverseDiscrete Fourier Transform matrix or an oversampled Inverse DiscreteFourier Transform matrix.
 21. The apparatus according to claim 19,wherein the controller determines precoders based on the at least twoline of sight channel parameters; and applies the precoders to theantenna array.
 22. The apparatus according to claim 19, wherein thecontroller extracts by forming a least-squares estimate of the at leasttwo line of sight channel parameters based on the channel matrix. 23.The apparatus according to claim 19, wherein the controller adjusts arotation of the antenna array based on at least one of the line of sightchannel parameters.
 24. The apparatus according to claim 19, wherein thecontroller determines a subset of transmitting device antennas thatyield improved line of sight capacity over a set of transmitting deviceantennas based on at least one of the at least two line of sight channelparameters, and signals the subset of transmitting device antennas tothe transmitting device.
 25. The apparatus according to claim 19,wherein the controller evaluates at least one of the line of sightchannel parameters over a set of allowed wavelengths, and selects awavelength from the set of allowed wavelengths that yields the channelmatrix with the largest capacity.
 26. The apparatus according to claim18, wherein the controller selects an inverted channel mode oftransmission based on a line of sight channel parameter beingapproximately equal to a reciprocal of a number of antennas in an arrayof antennas of the transmitting device.